-
Previous Article
On the homogenization of some non-coercive Hamilton--Jacobi--Isaacs equations
- CPAA Home
- This Issue
-
Next Article
A refined result on sign changing solutions for a critical elliptic problem
Existence theory for a Poisson-Nernst-Planck model of electrophoresis
1. | Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Trindade, Florianópolis-SC, Brazil, CEP 88040-900, Brazil |
2. | Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonáalves 9500, Porto Alegre-RS, Brazil, CEP 91509-900, Brazil |
References:
[1] |
S. A. Allison, C. Chen and D. Stigter, The length dependence of translational diffusion, free solution electrophoretic mobility, and electrophoretic tether force of rigid rod-like model duplex DNA, Biophys. J., 81 (2001), 2558-2568.
doi: 10.1016/S0006-3495(01)75900-0. |
[2] |
S. A. Allison and D. Stigter, A commentary on the screened-Oseen, counterion-condensation formalism of polyion electrophoresis, Biophys. J., 78 (2000), 121-124.
doi: 10.1016/S0006-3495(00)76578-7. |
[3] |
J. L. Anderson, Colloidal transport by interfacial forces, Ann. Rev. Fluid Mech., 21 (1989), 61-99.
doi: 10.1146/annurev.fl.21.010189.000425. |
[4] |
L. Bedin and M. Thompson, Motion of a charged particle in ionized fluids, Math. Models & Meth. Appl. Sci., 16 (2006), 1271-1318.
doi: 10.1142/S0218202506001546. |
[5] |
L. Bedin and M. Thompson, Weak solutions for the electrophoretic motion of charged Particles, Comp. & App. Math., 25 (2006), 1-26.
doi: 10.1590/S0101-82052006000100001. |
[6] |
H. Brézis, "Análisis Funcional: Teoría y Aplicaciones," Alianza Editorial, Madrid, 1984. |
[7] |
Z. Chen and J. Zou, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math., 79 (1998), 175-202.
doi: 10.1007/s002110050336. |
[8] |
W. L. Cheng, Y. Y. He and E. Lee, Electrophoresis of a soft particle normal to a plane, J. Colloid Interface Sci., 335 (2009), 130-139.
doi: 10.1016/j.jcis.2009.02.051. |
[9] |
Y. S. Choi and S. J. Kim, Electrokinetic flow-induced currents in silica nanofluidic channels, J. Colloid Interface Sci., 333 (2009), 672-678.
doi: 10.1016/j.jcis.2009.01.061. |
[10] |
D. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," Krieger, Malabar, 1992. |
[11] |
C. M. Cortis and R. A. Friesner, An automatic three-dimensional finit element mesh generation system for the Poisson-Boltzmann equation, J. Comp. Chem., 18 (1997), 1570-1590.
doi: 10.1002/(SICI)1096-987X(199710)18:13<1570::AID-JCC2>3.0.CO;2-O. |
[12] |
M. Daune, "Molecular Biophysics: Structures in Motion," Oxford University Press, New York, 1999. |
[13] |
B. Desjardins, Weak solutions of the compressible isentropic Navier-Stokes equations, App. Math. Letters, 12 (1999), 107-111.
doi: 10.1016/S0893-9659(99)00109-3. |
[14] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Rational Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[15] |
B. Desjardins and M. J. Esteban, On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, Comm. Partial Diff. Eq., 25 (2000), 1399-1414.
doi: 10.1080/03605300008821553. |
[16] |
R. J. Di Perna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[17] | |
[18] |
M. Fixman, Charged macromolecules in external fields I. The sphere, J. Chem. Phys., 72 (1980), 5177-5186.
doi: 10.1063/1.439753. |
[19] |
A. Friedman, "Partial Differential Equations of Parabolic Type," Dover, New York, 2008. |
[20] |
L. M. Fu, R. J. Yang and G. B. Lee, Analysis of geometry effects on band spreading of microchip electrophoresis, Electrophoresis, 23 (2002), 602-612.
doi: 10.1002/1522-2683(200202)23:4<602::AID-ELPS602>3.0.CO;2-N. |
[21] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[22] |
W. Hackbusch, "Integral Equations: Theory and Numerical Treatment," Birkhäuser Verlag, Basel, 1995. |
[23] |
J. Huang and J. Zou, Some new a priori estimates for second-order elliptic and parabolic interface problems, J. Diff. Equations, 184 (2002), 570-586.
doi: 10.1006/jdeq.2001.4154. |
[24] |
H. J. Keh and J. L. Anderson, Boundary effects on electrophoretic motion of colloidal spheres, J. Fluid Mech., 153 (1985), 417-439.
doi: 10.1017/S002211208500132X. |
[25] |
J. Y. Kim and B. J. Yoon, Electrophoretic motion of a slightly deformed sphere with a nonuniform zeta potential distribution, J. Colloid Interface Sci., 251 (2002), 318-330.
doi: 10.1006/jcis.2002.8359. |
[26] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasi-Linear Equations of Parabolic Type," AMS, Providence, 1988. |
[27] |
O. A. Ladyženskaja and N. N. Ural'ceva, "Linear and Quasi-Linear Elliptic Equations," Academic Press, New York-London, 1968. |
[28] |
B. Lu, Y. C. Zhou, G. A. Huber, S. D. Bond, M. J. Holst and J. A. McCannon, Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution, J. Chem. Phys., 127 (2007), 1-17.
doi: 10.1063/1.2775933. |
[29] |
H. Nakamura, Roles of electrostatic interaction in proteins, Quart. Rev. Biophys, 29 (1996), 1-90.
doi: 10.1017/S0033583500005746. |
[30] |
J. Necăs, "Les Méthodes Directes en Théorie des Équations Elliptiques," Masson Et Cie, Paris, 1967. |
[31] |
H. M. Park, J. S. Lee and T. W. Kim, Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels, J. Colloid Interface Sci., 315 (2007), 731-739.
doi: 10.1016/j.jcis.2007.07.007. |
[32] |
A. Quarteroni and A., Valli, "Numerical Approximation of Partial Differential Equations," Springer, Berlin, 1994. |
[33] |
S. Qian, A. Wang and J. K. Afonien, Electrophoretic motion of a spherical particle in a converging-diverging nanotube, J. Colloid Interface Sci., 303 (2006), 579-592.
doi: 10.1016/j.jcis.2006.08.003. |
[34] |
S. E. Reiner and C. J. Radke, Variational Approach to the Electrostatic Free Energy in Charged Colloidal Suspensions: General Theory for Open Systems, J. Chem. Faraday Trans., 86 (1990), 3901-3912.
doi: 10.1039/FT9908603901. |
[35] |
W. B. Russel, D. A. Saville and W. R. Schowalter, "Colloidal Dispersions," Cambridge University Press, 1995. |
[36] |
A. Sellier, A note on the electrophoresis of a uniformly charged particle, Q. J. Mech. Appl. Math., 55 (2002), 561-572.
doi: 10.1093/qjmam/55.4.561. |
[37] |
M. Schmuck, Analysis of the Navier-Stokes-Nernst-Planck-Poisson system, Math. Models & Meth. Appl. Sci., 19 (2009), 993-1015.
doi: 10.1142/S0218202509003693. |
[38] |
A. A. Shugai and S. L. Carnie, Electrophoretic motion of a spherical particle with a thick double layer in bounded flows, J. Colloid Interface Sci., 213 (1999), 298-315.
doi: 10.1006/jcis.1999.6143. |
[39] |
Y. Solomentsev and J. L. Anderson, Electrophoresis of slender particles, J. Fluid Mech., 279 (1994), 197-215.
doi: 10.1017/S0022112094003885. |
[40] |
M. Teubner, The motion of charged particles in electrical fields, J. Chem. Phys., 76 (1982), 5564-5573.
doi: 10.1063/1.442861. |
show all references
References:
[1] |
S. A. Allison, C. Chen and D. Stigter, The length dependence of translational diffusion, free solution electrophoretic mobility, and electrophoretic tether force of rigid rod-like model duplex DNA, Biophys. J., 81 (2001), 2558-2568.
doi: 10.1016/S0006-3495(01)75900-0. |
[2] |
S. A. Allison and D. Stigter, A commentary on the screened-Oseen, counterion-condensation formalism of polyion electrophoresis, Biophys. J., 78 (2000), 121-124.
doi: 10.1016/S0006-3495(00)76578-7. |
[3] |
J. L. Anderson, Colloidal transport by interfacial forces, Ann. Rev. Fluid Mech., 21 (1989), 61-99.
doi: 10.1146/annurev.fl.21.010189.000425. |
[4] |
L. Bedin and M. Thompson, Motion of a charged particle in ionized fluids, Math. Models & Meth. Appl. Sci., 16 (2006), 1271-1318.
doi: 10.1142/S0218202506001546. |
[5] |
L. Bedin and M. Thompson, Weak solutions for the electrophoretic motion of charged Particles, Comp. & App. Math., 25 (2006), 1-26.
doi: 10.1590/S0101-82052006000100001. |
[6] |
H. Brézis, "Análisis Funcional: Teoría y Aplicaciones," Alianza Editorial, Madrid, 1984. |
[7] |
Z. Chen and J. Zou, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math., 79 (1998), 175-202.
doi: 10.1007/s002110050336. |
[8] |
W. L. Cheng, Y. Y. He and E. Lee, Electrophoresis of a soft particle normal to a plane, J. Colloid Interface Sci., 335 (2009), 130-139.
doi: 10.1016/j.jcis.2009.02.051. |
[9] |
Y. S. Choi and S. J. Kim, Electrokinetic flow-induced currents in silica nanofluidic channels, J. Colloid Interface Sci., 333 (2009), 672-678.
doi: 10.1016/j.jcis.2009.01.061. |
[10] |
D. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," Krieger, Malabar, 1992. |
[11] |
C. M. Cortis and R. A. Friesner, An automatic three-dimensional finit element mesh generation system for the Poisson-Boltzmann equation, J. Comp. Chem., 18 (1997), 1570-1590.
doi: 10.1002/(SICI)1096-987X(199710)18:13<1570::AID-JCC2>3.0.CO;2-O. |
[12] |
M. Daune, "Molecular Biophysics: Structures in Motion," Oxford University Press, New York, 1999. |
[13] |
B. Desjardins, Weak solutions of the compressible isentropic Navier-Stokes equations, App. Math. Letters, 12 (1999), 107-111.
doi: 10.1016/S0893-9659(99)00109-3. |
[14] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Rational Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[15] |
B. Desjardins and M. J. Esteban, On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, Comm. Partial Diff. Eq., 25 (2000), 1399-1414.
doi: 10.1080/03605300008821553. |
[16] |
R. J. Di Perna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[17] | |
[18] |
M. Fixman, Charged macromolecules in external fields I. The sphere, J. Chem. Phys., 72 (1980), 5177-5186.
doi: 10.1063/1.439753. |
[19] |
A. Friedman, "Partial Differential Equations of Parabolic Type," Dover, New York, 2008. |
[20] |
L. M. Fu, R. J. Yang and G. B. Lee, Analysis of geometry effects on band spreading of microchip electrophoresis, Electrophoresis, 23 (2002), 602-612.
doi: 10.1002/1522-2683(200202)23:4<602::AID-ELPS602>3.0.CO;2-N. |
[21] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[22] |
W. Hackbusch, "Integral Equations: Theory and Numerical Treatment," Birkhäuser Verlag, Basel, 1995. |
[23] |
J. Huang and J. Zou, Some new a priori estimates for second-order elliptic and parabolic interface problems, J. Diff. Equations, 184 (2002), 570-586.
doi: 10.1006/jdeq.2001.4154. |
[24] |
H. J. Keh and J. L. Anderson, Boundary effects on electrophoretic motion of colloidal spheres, J. Fluid Mech., 153 (1985), 417-439.
doi: 10.1017/S002211208500132X. |
[25] |
J. Y. Kim and B. J. Yoon, Electrophoretic motion of a slightly deformed sphere with a nonuniform zeta potential distribution, J. Colloid Interface Sci., 251 (2002), 318-330.
doi: 10.1006/jcis.2002.8359. |
[26] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasi-Linear Equations of Parabolic Type," AMS, Providence, 1988. |
[27] |
O. A. Ladyženskaja and N. N. Ural'ceva, "Linear and Quasi-Linear Elliptic Equations," Academic Press, New York-London, 1968. |
[28] |
B. Lu, Y. C. Zhou, G. A. Huber, S. D. Bond, M. J. Holst and J. A. McCannon, Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution, J. Chem. Phys., 127 (2007), 1-17.
doi: 10.1063/1.2775933. |
[29] |
H. Nakamura, Roles of electrostatic interaction in proteins, Quart. Rev. Biophys, 29 (1996), 1-90.
doi: 10.1017/S0033583500005746. |
[30] |
J. Necăs, "Les Méthodes Directes en Théorie des Équations Elliptiques," Masson Et Cie, Paris, 1967. |
[31] |
H. M. Park, J. S. Lee and T. W. Kim, Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels, J. Colloid Interface Sci., 315 (2007), 731-739.
doi: 10.1016/j.jcis.2007.07.007. |
[32] |
A. Quarteroni and A., Valli, "Numerical Approximation of Partial Differential Equations," Springer, Berlin, 1994. |
[33] |
S. Qian, A. Wang and J. K. Afonien, Electrophoretic motion of a spherical particle in a converging-diverging nanotube, J. Colloid Interface Sci., 303 (2006), 579-592.
doi: 10.1016/j.jcis.2006.08.003. |
[34] |
S. E. Reiner and C. J. Radke, Variational Approach to the Electrostatic Free Energy in Charged Colloidal Suspensions: General Theory for Open Systems, J. Chem. Faraday Trans., 86 (1990), 3901-3912.
doi: 10.1039/FT9908603901. |
[35] |
W. B. Russel, D. A. Saville and W. R. Schowalter, "Colloidal Dispersions," Cambridge University Press, 1995. |
[36] |
A. Sellier, A note on the electrophoresis of a uniformly charged particle, Q. J. Mech. Appl. Math., 55 (2002), 561-572.
doi: 10.1093/qjmam/55.4.561. |
[37] |
M. Schmuck, Analysis of the Navier-Stokes-Nernst-Planck-Poisson system, Math. Models & Meth. Appl. Sci., 19 (2009), 993-1015.
doi: 10.1142/S0218202509003693. |
[38] |
A. A. Shugai and S. L. Carnie, Electrophoretic motion of a spherical particle with a thick double layer in bounded flows, J. Colloid Interface Sci., 213 (1999), 298-315.
doi: 10.1006/jcis.1999.6143. |
[39] |
Y. Solomentsev and J. L. Anderson, Electrophoresis of slender particles, J. Fluid Mech., 279 (1994), 197-215.
doi: 10.1017/S0022112094003885. |
[40] |
M. Teubner, The motion of charged particles in electrical fields, J. Chem. Phys., 76 (1982), 5564-5573.
doi: 10.1063/1.442861. |
[1] |
Kuijie Li, Tohru Ozawa, Baoxiang Wang. Dynamical behavior for the solutions of the Navier-Stokes equation. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1511-1560. doi: 10.3934/cpaa.2018073 |
[2] |
C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403 |
[3] |
Minghua Yang, Jinyi Sun. Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1617-1639. doi: 10.3934/cpaa.2017078 |
[4] |
Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237 |
[5] |
I. Moise, Roger Temam. Renormalization group method: Application to Navier-Stokes equation. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 191-210. doi: 10.3934/dcds.2000.6.191 |
[6] |
Igor Kukavica, Mohammed Ziane. Regularity of the Navier-Stokes equation in a thin periodic domain with large data. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 67-86. doi: 10.3934/dcds.2006.16.67 |
[7] |
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 |
[8] |
Hyung Ju Hwang, Juhi Jang. On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 681-691. doi: 10.3934/dcdsb.2013.18.681 |
[9] |
Anna Amirdjanova, Jie Xiong. Large deviation principle for a stochastic navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 651-666. doi: 10.3934/dcdsb.2006.6.651 |
[10] |
Fuzhi Li, Dongmei Xu, Jiali Yu. Regular measurable backward compact random attractor for $ g $-Navier-Stokes equation. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3137-3157. doi: 10.3934/cpaa.2020136 |
[11] |
Boris Haspot, Ewelina Zatorska. From the highly compressible Navier-Stokes equations to the porous medium equation -- rate of convergence. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3107-3123. doi: 10.3934/dcds.2016.36.3107 |
[12] |
Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations and Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1 |
[13] |
Sun-Ho Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible Navier-Stokes equation. Networks and Heterogeneous Media, 2013, 8 (2) : 465-479. doi: 10.3934/nhm.2013.8.465 |
[14] |
Jingrui Wang, Keyan Wang. Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 5003-5019. doi: 10.3934/dcds.2017215 |
[15] |
Leanne Dong. Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5421-5448. doi: 10.3934/dcdsb.2020352 |
[16] |
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 |
[17] |
Hongyong Cui, Mirelson M. Freitas, José A. Langa. Squeezing and finite dimensionality of cocycle attractors for 2D stochastic Navier-Stokes equation with non-autonomous forcing. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1297-1324. doi: 10.3934/dcdsb.2018152 |
[18] |
Fuzhi Li, Dongmei Xu. Asymptotically autonomous dynamics for non-autonomous stochastic $ g $-Navier-Stokes equation with additive noise. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022087 |
[19] |
Chia-Yu Hsieh. Stability of radial solutions of the Poisson-Nernst-Planck system in annular domains. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2657-2681. doi: 10.3934/dcdsb.2018269 |
[20] |
Mohamad Rachid. Incompressible Navier-Stokes-Fourier limit from the Landau equation. Kinetic and Related Models, 2021, 14 (4) : 599-638. doi: 10.3934/krm.2021017 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]