-
Previous Article
Multiplicity of subharmonic solutions and periodic solutions of a particular type of super-quadratic Hamiltonian systems
- CPAA Home
- This Issue
-
Next Article
Scattering for a nonlinear Schrödinger equation with a potential
Decay of the compressible viscoelastic flows
1. | Department of Mathematics, Guizou University, Guiyang, Guizhou Province |
2. | School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China |
3. | Department of Mathematics, Sun Yat-sen University, Guangzhou 510275 |
References:
[1] |
J. Y. Chemin and N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal., 33 (2001), 84-112.
doi: 10.1137/S0036141099359317. |
[2] |
K. Deckelnick, Decay estimates for the compressible Navier-Stokes equations in unbounded domains, Math. Z., 209 (1992), 115-130.
doi: 10.1007/BF02570825. |
[3] |
K. Deckelnick, $L^{2}$-decay for the compressible Navier-Stokes equations in unbounded domains, Commun. Partial Differ. Equ., 18 (1993), 1445-1476.
doi: 10.1080/03605309308820981. |
[4] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal $L^p-L^q$ convergence rate for the compressible Navier-Stokes equations with potential force, J. Differential Equations, 238 (2007), 220-223. |
[5] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal convergence rate for compressible Navier-Stokes equations with potential force, Math. Models. Methods Appl. Sci., 17 (2007), 737-758.
doi: 10.1142/S021820250700208X. |
[6] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[7] |
X. P. Hu and D. H. Wang, Local strong solution to the compressible viscoelastic flow with large data, J. Differential Equations, 249 (2010), 1179-1198.
doi: 10.1016/j.jde.2010.03.027. |
[8] |
X. P. Hu and D. H. Wang, Global existence for the multi-dimensional compressible viscoelastic flows, J. Differential Equations, 250 (2011), 1200-1231.
doi: 10.1016/j.jde.2010.10.017. |
[9] |
X. P. Hu and G. C. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833.
doi: 10.1137/120892350. |
[10] |
X. P. Hu and H. Wu, Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 3437-3461. |
[11] |
T. Kobayashi and Y. Shibata, Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in $R^{3}$, Commun. Math. Phys., 200 (1999), 621-659.
doi: 10.1007/s002200050543. |
[12] |
T. Kobayashi and Y. Shibata, Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations, Pacific J. Math., 207 (2002), 199-234.
doi: 10.2140/pjm.2002.207.199. |
[13] |
F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math., 58 (2005), 1437-1471.
doi: 10.1002/cpa.20074. |
[14] |
Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain, Comm. Math. Sci., 5 (2007), 595-616. |
[15] |
P. L. Lions and N. Masmoudi, Global solutions for some Oldroyd models of non-Newtonian flows, Chinese Ann. Math. Ser. B, 21 (2000), 131-146.
doi: 10.1142/S0252959900000170. |
[16] |
T. P. Liu and W. K. Wang, The pointwise estiamtes of diffusion waves for Navier-Stokes equations in odd multi-dimensions, Commun. Math. Phys., 196 (1998), 145-173.
doi: 10.1007/s002200050418. |
[17] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[18] |
J. Z. Qian and Z. F. Zhang, Global well-posedness for the compressible viscoelastic fluids near equilibrium, Arch. Ration. Mech. Anal., 198 (2010), 835-868.
doi: 10.1007/s00205-010-0351-5. |
[19] |
M. E. Schonbek, $L^{2}$ decay of weak solutions of the Navier-Stokes equations, Arch. Ration. Mech. Anal., 88 (1985), 209-222.
doi: 10.1007/BF00752111. |
[20] |
M. E. Schonbek, Large time behaviour of solutions of the Navier-Stokes equations, Comm. Partial Differential Equations, 11 (1986), 733-763.
doi: 10.1080/03605308608820443. |
[21] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. |
[22] |
T. Zhang and D. Y. Fang, Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical $L^p$ framework, SIAM J. Math. Anal., 44 (2012), 2266-2288.
doi: 10.1137/110851742. |
[23] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Differential Equations, 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[24] |
Y. J. Wang and Z. Tan, Global existence and optimal decay rate for the strong solutions in $H^{2}$ to the compressible Navier-Stokes equations, Appl. Math. Lett., 24 (2011), 1778-1784.
doi: 10.1016/j.aml.2011.04.028. |
show all references
References:
[1] |
J. Y. Chemin and N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal., 33 (2001), 84-112.
doi: 10.1137/S0036141099359317. |
[2] |
K. Deckelnick, Decay estimates for the compressible Navier-Stokes equations in unbounded domains, Math. Z., 209 (1992), 115-130.
doi: 10.1007/BF02570825. |
[3] |
K. Deckelnick, $L^{2}$-decay for the compressible Navier-Stokes equations in unbounded domains, Commun. Partial Differ. Equ., 18 (1993), 1445-1476.
doi: 10.1080/03605309308820981. |
[4] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal $L^p-L^q$ convergence rate for the compressible Navier-Stokes equations with potential force, J. Differential Equations, 238 (2007), 220-223. |
[5] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal convergence rate for compressible Navier-Stokes equations with potential force, Math. Models. Methods Appl. Sci., 17 (2007), 737-758.
doi: 10.1142/S021820250700208X. |
[6] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[7] |
X. P. Hu and D. H. Wang, Local strong solution to the compressible viscoelastic flow with large data, J. Differential Equations, 249 (2010), 1179-1198.
doi: 10.1016/j.jde.2010.03.027. |
[8] |
X. P. Hu and D. H. Wang, Global existence for the multi-dimensional compressible viscoelastic flows, J. Differential Equations, 250 (2011), 1200-1231.
doi: 10.1016/j.jde.2010.10.017. |
[9] |
X. P. Hu and G. C. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833.
doi: 10.1137/120892350. |
[10] |
X. P. Hu and H. Wu, Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 3437-3461. |
[11] |
T. Kobayashi and Y. Shibata, Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in $R^{3}$, Commun. Math. Phys., 200 (1999), 621-659.
doi: 10.1007/s002200050543. |
[12] |
T. Kobayashi and Y. Shibata, Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations, Pacific J. Math., 207 (2002), 199-234.
doi: 10.2140/pjm.2002.207.199. |
[13] |
F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math., 58 (2005), 1437-1471.
doi: 10.1002/cpa.20074. |
[14] |
Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain, Comm. Math. Sci., 5 (2007), 595-616. |
[15] |
P. L. Lions and N. Masmoudi, Global solutions for some Oldroyd models of non-Newtonian flows, Chinese Ann. Math. Ser. B, 21 (2000), 131-146.
doi: 10.1142/S0252959900000170. |
[16] |
T. P. Liu and W. K. Wang, The pointwise estiamtes of diffusion waves for Navier-Stokes equations in odd multi-dimensions, Commun. Math. Phys., 196 (1998), 145-173.
doi: 10.1007/s002200050418. |
[17] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[18] |
J. Z. Qian and Z. F. Zhang, Global well-posedness for the compressible viscoelastic fluids near equilibrium, Arch. Ration. Mech. Anal., 198 (2010), 835-868.
doi: 10.1007/s00205-010-0351-5. |
[19] |
M. E. Schonbek, $L^{2}$ decay of weak solutions of the Navier-Stokes equations, Arch. Ration. Mech. Anal., 88 (1985), 209-222.
doi: 10.1007/BF00752111. |
[20] |
M. E. Schonbek, Large time behaviour of solutions of the Navier-Stokes equations, Comm. Partial Differential Equations, 11 (1986), 733-763.
doi: 10.1080/03605308608820443. |
[21] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. |
[22] |
T. Zhang and D. Y. Fang, Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical $L^p$ framework, SIAM J. Math. Anal., 44 (2012), 2266-2288.
doi: 10.1137/110851742. |
[23] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Differential Equations, 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[24] |
Y. J. Wang and Z. Tan, Global existence and optimal decay rate for the strong solutions in $H^{2}$ to the compressible Navier-Stokes equations, Appl. Math. Lett., 24 (2011), 1778-1784.
doi: 10.1016/j.aml.2011.04.028. |
[1] |
Vianney Perchet, Marc Quincampoix. A differential game on Wasserstein space. Application to weak approachability with partial monitoring. Journal of Dynamics and Games, 2019, 6 (1) : 65-85. doi: 10.3934/jdg.2019005 |
[2] |
Wen-ming He, Jun-zhi Cui. The estimate of the multi-scale homogenization method for Green's function on Sobolev space $W^{1,q}(\Omega)$. Communications on Pure and Applied Analysis, 2012, 11 (2) : 501-516. doi: 10.3934/cpaa.2012.11.501 |
[3] |
Martin Bauer, Philipp Harms, Peter W. Michor. Sobolev metrics on shape space of surfaces. Journal of Geometric Mechanics, 2011, 3 (4) : 389-438. doi: 10.3934/jgm.2011.3.389 |
[4] |
Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 745-767. doi: 10.3934/dcdss.2020365 |
[5] |
Rowan Killip, Satoshi Masaki, Jason Murphy, Monica Visan. The radial mass-subcritical NLS in negative order Sobolev spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 553-583. doi: 10.3934/dcds.2019023 |
[6] |
Yunho Kim, Luminita A. Vese. Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability. Inverse Problems and Imaging, 2009, 3 (1) : 43-68. doi: 10.3934/ipi.2009.3.43 |
[7] |
Kazumasa Fujiwara, Shuji Machihara, Tohru Ozawa. On a system of semirelativistic equations in the energy space. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1343-1355. doi: 10.3934/cpaa.2015.14.1343 |
[8] |
Kazumasa Fujiwara, Shuji Machihara, Tohru Ozawa. Remark on a semirelativistic equation in the energy space. Conference Publications, 2015, 2015 (special) : 473-478. doi: 10.3934/proc.2015.0473 |
[9] |
Martins Bruveris. Completeness properties of Sobolev metrics on the space of curves. Journal of Geometric Mechanics, 2015, 7 (2) : 125-150. doi: 10.3934/jgm.2015.7.125 |
[10] |
Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková. Sharp Sobolev type embeddings on the entire Euclidean space. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2011-2037. doi: 10.3934/cpaa.2018096 |
[11] |
Kun Wang, Yinnian He, Yanping Lin. Long time numerical stability and asymptotic analysis for the viscoelastic Oldroyd flows. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1551-1573. doi: 10.3934/dcdsb.2012.17.1551 |
[12] |
Wenjing Zhao. Weak-strong uniqueness of incompressible magneto-viscoelastic flows. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2907-2917. doi: 10.3934/cpaa.2020127 |
[13] |
Colette Guillopé, Zaynab Salloum, Raafat Talhouk. Regular flows of weakly compressible viscoelastic fluids and the incompressible limit. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1001-1028. doi: 10.3934/dcdsb.2010.14.1001 |
[14] |
Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917 |
[15] |
Xiaoxiao Li, Yingjing Shi, Rui Li, Shida Cao. Energy management method for an unpowered landing. Journal of Industrial and Management Optimization, 2022, 18 (2) : 825-841. doi: 10.3934/jimo.2020180 |
[16] |
Kotaro Tsugawa. Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index. Communications on Pure and Applied Analysis, 2004, 3 (2) : 301-318. doi: 10.3934/cpaa.2004.3.301 |
[17] |
Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665 |
[18] |
Salim A. Messaoudi, Ala A. Talahmeh. Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1233-1245. doi: 10.3934/dcdss.2021107 |
[19] |
Irena Pawłow, Wojciech M. Zajączkowski. Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm. Discrete and Continuous Dynamical Systems - S, 2011, 4 (2) : 441-466. doi: 10.3934/dcdss.2011.4.441 |
[20] |
Anouar Bahrouni, VicenŢiu D. RĂdulescu. On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 379-389. doi: 10.3934/dcdss.2018021 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]