-
Previous Article
A general stability result in a memory-type Timoshenko system
- CPAA Home
- This Issue
-
Next Article
Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion
Weak solutions for generalized large-scale semigeostrophic equations
1. | School of Engineering and Science, Jacobs University, 28759 Bremen, Germany |
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables,'' tenth edition, Dover, New York, 1972. |
[2] |
R. A. Adams and J. J. F Fournier, "Sobolev Spaces,'' second edition, Elsevier, Oxford, 2003. |
[3] |
C. Bardos, Existence et unicité de la solution de l'équation d'Euler en dimension deux, J. Math. Anal. and Appl., 40 (1972), 769-790. |
[4] |
Y.-Z. Chen and L.-C. Wu, "Second Order Elliptic Equations and Elliptic Systems,'' AMS, Providence, RI, 1998. |
[5] |
M. Çalık, M. Oliver and S. Vasylkevych, Global well-posedness for the generalized large-scale semigeostrophic equations, Arch. Ration. Mech. An., accepted for publication, 2012. |
[6] |
C. R. Doering, J. D. Gibbon and C. D. Levermore, Weak and strong solutions of the complex Ginzburg-Landau equation, Phys. D, 71 (1994), 285-318.
doi: 10.1016/0167-2789(94)90150-3. |
[7] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,'' Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. |
[8] |
D. D. Holm, Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion, Phys. D, 133 (1999), 215-269.
doi: 10.1016/S0167-2789(99)00093-7. |
[9] |
D. D. Holm, J. E. Marsden and T. S. Ratiu, Euler-Poincaré equations and semidirect products with applications to continuum theories, Adv. in Math., 137 (1998), 1-81.
doi: 10.1006/aima.1998.1721. |
[10] |
E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Sitzungsber. d. Preuss. Acad. Wiss., 19 (1927), 147-152. |
[11] |
C. D. Levermore, M. Oliver and E. S. Titi, Global well-posedness for models of shallow water in a basin of varying bottom, Indiana Univ. Math. J., 45 (1996), 479-510. |
[12] |
J. Marsden and S. Shkoller, Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations on bounded domains, Phil. Trans R. Soc Lond. A, 359 (2001), 1449-1468.
doi: 10.1098/rsta.2001.0852. |
[13] |
M. Oliver, Variational asymptotics for rotating shallow water near geostrophy: A transformational approach, J. Fluid Mech., 551 (2006), 197-234.
doi: 10.1017/S0022112005008256. |
[14] |
M. Oliver and S. Shkoller, The vortex blob method as a second-grade non-Newtonian fluid, Comm. in Part. Diff. Eq., 26 (2001), 295-314. |
[15] |
M. Oliver and S. Vasylkevych, Hamiltonian formalism for models of rotating shallow water in semigeostrophic scaling, Discr. Cont. Dyn. Sys., 31 (2011), 827-846.
doi: 10.3934/dcds.2011.31.827. |
[16] |
M. Oliver and S. Vasylkevych, Generalized LSG models with varying Coriolis parameter,, Geophys. Astrophys. Fluid Dyn., ().
|
[17] |
R. Salmon, New equations for nearly geostrophic flow, J. Fluid Mech., 153 (1985), 461-477.
doi: 10.1017/S0022112085001343. |
[18] |
V. I. Yudovich, Some bounds for solutions of elliptic equations, Amer. Math. Soc. Transl. Ser. 2, Vol. 56 (1966); previously in Mat. Sb. (N.S.), 59 (1962), suppl. 229-244 (in Russian). |
[19] |
V. I. Yudovich, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz., 6 (1963), 1032-1066. |
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables,'' tenth edition, Dover, New York, 1972. |
[2] |
R. A. Adams and J. J. F Fournier, "Sobolev Spaces,'' second edition, Elsevier, Oxford, 2003. |
[3] |
C. Bardos, Existence et unicité de la solution de l'équation d'Euler en dimension deux, J. Math. Anal. and Appl., 40 (1972), 769-790. |
[4] |
Y.-Z. Chen and L.-C. Wu, "Second Order Elliptic Equations and Elliptic Systems,'' AMS, Providence, RI, 1998. |
[5] |
M. Çalık, M. Oliver and S. Vasylkevych, Global well-posedness for the generalized large-scale semigeostrophic equations, Arch. Ration. Mech. An., accepted for publication, 2012. |
[6] |
C. R. Doering, J. D. Gibbon and C. D. Levermore, Weak and strong solutions of the complex Ginzburg-Landau equation, Phys. D, 71 (1994), 285-318.
doi: 10.1016/0167-2789(94)90150-3. |
[7] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,'' Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. |
[8] |
D. D. Holm, Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion, Phys. D, 133 (1999), 215-269.
doi: 10.1016/S0167-2789(99)00093-7. |
[9] |
D. D. Holm, J. E. Marsden and T. S. Ratiu, Euler-Poincaré equations and semidirect products with applications to continuum theories, Adv. in Math., 137 (1998), 1-81.
doi: 10.1006/aima.1998.1721. |
[10] |
E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Sitzungsber. d. Preuss. Acad. Wiss., 19 (1927), 147-152. |
[11] |
C. D. Levermore, M. Oliver and E. S. Titi, Global well-posedness for models of shallow water in a basin of varying bottom, Indiana Univ. Math. J., 45 (1996), 479-510. |
[12] |
J. Marsden and S. Shkoller, Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations on bounded domains, Phil. Trans R. Soc Lond. A, 359 (2001), 1449-1468.
doi: 10.1098/rsta.2001.0852. |
[13] |
M. Oliver, Variational asymptotics for rotating shallow water near geostrophy: A transformational approach, J. Fluid Mech., 551 (2006), 197-234.
doi: 10.1017/S0022112005008256. |
[14] |
M. Oliver and S. Shkoller, The vortex blob method as a second-grade non-Newtonian fluid, Comm. in Part. Diff. Eq., 26 (2001), 295-314. |
[15] |
M. Oliver and S. Vasylkevych, Hamiltonian formalism for models of rotating shallow water in semigeostrophic scaling, Discr. Cont. Dyn. Sys., 31 (2011), 827-846.
doi: 10.3934/dcds.2011.31.827. |
[16] |
M. Oliver and S. Vasylkevych, Generalized LSG models with varying Coriolis parameter,, Geophys. Astrophys. Fluid Dyn., ().
|
[17] |
R. Salmon, New equations for nearly geostrophic flow, J. Fluid Mech., 153 (1985), 461-477.
doi: 10.1017/S0022112085001343. |
[18] |
V. I. Yudovich, Some bounds for solutions of elliptic equations, Amer. Math. Soc. Transl. Ser. 2, Vol. 56 (1966); previously in Mat. Sb. (N.S.), 59 (1962), suppl. 229-244 (in Russian). |
[19] |
V. I. Yudovich, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz., 6 (1963), 1032-1066. |
[1] |
Igor Chueshov, Irena Lasiecka. Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 777-809. doi: 10.3934/dcds.2006.15.777 |
[2] |
Xiaoyu Chen, Jijie Zhao, Qian Zhang. Global existence of weak solutions for the 3D axisymmetric chemotaxis-Navier-Stokes equations with nonlinear diffusion. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022062 |
[3] |
John W. Barrett, Endre Süli. Existence of global weak solutions to Fokker-Planck and Navier-Stokes-Fokker-Planck equations in kinetic models of dilute polymers. Discrete and Continuous Dynamical Systems - S, 2010, 3 (3) : 371-408. doi: 10.3934/dcdss.2010.3.371 |
[4] |
Yuming Chu, Yihang Hao, Xiangao Liu. Global weak solutions to a general liquid crystals system. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2681-2710. doi: 10.3934/dcds.2013.33.2681 |
[5] |
Zhenhua Guo, Mina Jiang, Zhian Wang, Gao-Feng Zheng. Global weak solutions to the Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 883-906. doi: 10.3934/dcds.2008.21.883 |
[6] |
Michael Röckner, Rongchan Zhu, Xiangchan Zhu. A remark on global solutions to random 3D vorticity equations for small initial data. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4021-4030. doi: 10.3934/dcdsb.2019048 |
[7] |
Xia Huang. Stable weak solutions of weighted nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2014, 13 (1) : 293-305. doi: 10.3934/cpaa.2014.13.293 |
[8] |
Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17 |
[9] |
Piotr Fijałkowski. A global inversion theorem for functions with singular points. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 173-180. doi: 10.3934/dcdsb.2018011 |
[10] |
Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867 |
[11] |
Hafedh Bousbih. Global weak solutions for a coupled chemotaxis non-Newtonian fluid. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 907-929. doi: 10.3934/dcdsb.2018212 |
[12] |
Shihui Zhu. Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5201-5221. doi: 10.3934/dcds.2016026 |
[13] |
Jonatan Lenells. Weak geodesic flow and global solutions of the Hunter-Saxton equation. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 643-656. doi: 10.3934/dcds.2007.18.643 |
[14] |
Bo Su and Martin Burger. Global weak solutions of non-isothermal front propagation problem. Electronic Research Announcements, 2007, 13: 46-52. |
[15] |
Zhen Lei, Yi Zhou. BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 575-583. doi: 10.3934/dcds.2009.25.575 |
[16] |
Bernard Ducomet, Eduard Feireisl, Hana Petzeltová, Ivan Straškraba. Global in time weak solutions for compressible barotropic self-gravitating fluids. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 113-130. doi: 10.3934/dcds.2004.11.113 |
[17] |
Chien-Hong Cho, Marcus Wunsch. Global weak solutions to the generalized Proudman-Johnson equation. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1387-1396. doi: 10.3934/cpaa.2012.11.1387 |
[18] |
Kristian Moring, Christoph Scheven, Sebastian Schwarzacher, Thomas Singer. Global higher integrability of weak solutions of porous medium systems. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1697-1745. doi: 10.3934/cpaa.2020069 |
[19] |
Cheng He, Changzheng Qu. Global weak solutions for the two-component Novikov equation. Electronic Research Archive, 2020, 28 (4) : 1545-1562. doi: 10.3934/era.2020081 |
[20] |
Fanqin Zeng, Yu Gao, Xiaoping Xue. Global weak solutions to the generalized mCH equation via characteristics. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021229 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]