-
Previous Article
On the Betti numbers of level sets of solutions to elliptic equations
- DCDS Home
- This Issue
-
Next Article
On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity
Global well-posedness of strong solutions to a tropical climate model
1. | Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel |
2. | Department of Mathematics, Texas A&M University, 3368-TAMU, College Station, TX 77843-3368, United States |
References:
[1] |
H. Brézis and T. Gallouet, Nonlinear Schrödinger evolution equations,, Nonlinear Anal., 4 (1980), 677.
doi: 10.1016/0362-546X(80)90068-1. |
[2] |
H. Brézis and S. Wainger, A Note on limiting cases of Sobolev embeddings and convolution inequalities,, Comm. Partial Differential Equations, 5 (1980), 773.
doi: 10.1080/03605308008820154. |
[3] |
C. Cao, S. Ibrahim, K. Nakanishi and E. S. Titi, Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics,, Comm. Math. Phys., 337 (2015), 473.
doi: 10.1007/s00220-015-2365-1. |
[4] |
C. Cao, J. Li and E. S. Titi, Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity,, Arch. Rational Mech. Anal., 214 (2014), 35.
doi: 10.1007/s00205-014-0752-y. |
[5] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity,, J. Differential Equations, 257 (2014), 4108.
doi: 10.1016/j.jde.2014.08.003. |
[6] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of the 3D primitive equations with only horizontal viscosity and diffusivity,, Comm. Pure Appl. Math., ().
doi: 10.1002/cpa.21576. |
[7] |
C. Cao, J. Li and E. S. Titi, Strong solutions to the 3D primitive equations with horizontal dissipation: near $H^1$ initial data,, preprint., (). Google Scholar |
[8] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of the 3D primitive equations with horizontal viscosities and vertical diffusion,, preprint., (). Google Scholar |
[9] |
C. Cao and E. S. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics,, Ann. of Math., 166 (2007), 245.
doi: 10.4007/annals.2007.166.245. |
[10] |
C. Cao and E. S. Titi, Global well-posedness of the 3D primitive equations with partial vertical turbulence mixing heat diffusion,, Comm. Math. Phys., 310 (2012), 537.
doi: 10.1007/s00220-011-1409-4. |
[11] |
R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables,, Ann. of Math., 103 (1976), 611.
doi: 10.2307/1970954. |
[12] |
R. R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals,, Trans. Amer. Math. Soc., 212 (1975), 315.
doi: 10.1090/S0002-9947-1975-0380244-8. |
[13] |
L. C. Evans, Partial Differential Equations,, $2^{nd}$ edition, (2010).
doi: 10.1090/gsm/019. |
[14] |
E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids,, Advances in Mathematical Fluid Mechanics, (2009).
doi: 10.1007/978-3-7643-8843-0. |
[15] |
D. M. W. Frierson, A. J. Majda and O. M. Pauluis, Large scale dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit,, Commun. Math. Sci., 2 (2004), 591.
doi: 10.4310/CMS.2004.v2.n4.a3. |
[16] |
A. E. Gill, Some simple solutions for heat-induced tropical circulation,, Quart. J. Roy. Meteor. Soc., 106 (1980), 447.
doi: 10.1002/qj.49710644905. |
[17] |
G. M. Kobelkov, Existence of a solution in the large for the 3D large-scale ocean dynamics equations,, C. R. Math. Acad. Sci. Paris, 343 (2006), 283.
doi: 10.1016/j.crma.2006.04.020. |
[18] |
I. Kukavica and M. Ziane, The regularity of solutions of the primitive equations of the ocean in space dimension three,, C. R. Math. Acad. Sci. Paris, 345 (2007), 257.
doi: 10.1016/j.crma.2007.07.025. |
[19] |
I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean,, Nonlinearity, 20 (2007), 2739.
doi: 10.1088/0951-7715/20/12/001. |
[20] |
A. Larios, E. Lunasin and E. S. Titi, Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion,, J. Differential Equations, 255 (2013), 2636.
doi: 10.1016/j.jde.2013.07.011. |
[21] |
J. Li and E. S. Titi, Global well-posedness of the 2D Boussinesq equations with vertical dissipation,, Arch. Ration. Mech. Anal., 220 (2016), 983.
doi: 10.1007/s00205-015-0946-y. |
[22] |
J. Li, E. S. Titi and Z. Xin, On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in $\mathbb R^2$,, Math. Models Methods Appl. Sci., 26 (2016), 803.
doi: 10.1142/S0218202516500184. |
[23] |
J. L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications,, Nonlinearity, 5 (1992), 237.
doi: 10.1088/0951-7715/5/2/001. |
[24] |
J. L. Lions, R. Temam and S. Wang, On the equations of the large-scale ocean,, Nonlinearity, 5 (1992), 1007.
doi: 10.1088/0951-7715/5/5/002. |
[25] |
J. L. Lions, R. Temam and S. Wang, Mathematical theory for the coupled atmosphere-ocean models (CAO III),, J. Math. Pures Appl., 74 (1995), 105.
|
[26] |
A. J. Majda and J. A. Biello, The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves,, J. Atmos. Sci., 60 (2003), 1809.
doi: 10.1175/1520-0469(2003)060<1809:TNIOBA>2.0.CO;2. |
[27] |
T. Matsuno, Quasi-geostrophic motions in the equatorial area,, J. Meteor. Soc. Japan, 44 (1966), 25. Google Scholar |
[28] |
T. K. Wong, Blowup of solutions of the hydrostatic Euler equations,, Proc. Amer. Math. Soc., 143 (2015), 1119.
doi: 10.1090/S0002-9939-2014-12243-X. |
show all references
References:
[1] |
H. Brézis and T. Gallouet, Nonlinear Schrödinger evolution equations,, Nonlinear Anal., 4 (1980), 677.
doi: 10.1016/0362-546X(80)90068-1. |
[2] |
H. Brézis and S. Wainger, A Note on limiting cases of Sobolev embeddings and convolution inequalities,, Comm. Partial Differential Equations, 5 (1980), 773.
doi: 10.1080/03605308008820154. |
[3] |
C. Cao, S. Ibrahim, K. Nakanishi and E. S. Titi, Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics,, Comm. Math. Phys., 337 (2015), 473.
doi: 10.1007/s00220-015-2365-1. |
[4] |
C. Cao, J. Li and E. S. Titi, Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity,, Arch. Rational Mech. Anal., 214 (2014), 35.
doi: 10.1007/s00205-014-0752-y. |
[5] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity,, J. Differential Equations, 257 (2014), 4108.
doi: 10.1016/j.jde.2014.08.003. |
[6] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of the 3D primitive equations with only horizontal viscosity and diffusivity,, Comm. Pure Appl. Math., ().
doi: 10.1002/cpa.21576. |
[7] |
C. Cao, J. Li and E. S. Titi, Strong solutions to the 3D primitive equations with horizontal dissipation: near $H^1$ initial data,, preprint., (). Google Scholar |
[8] |
C. Cao, J. Li and E. S. Titi, Global well-posedness of the 3D primitive equations with horizontal viscosities and vertical diffusion,, preprint., (). Google Scholar |
[9] |
C. Cao and E. S. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics,, Ann. of Math., 166 (2007), 245.
doi: 10.4007/annals.2007.166.245. |
[10] |
C. Cao and E. S. Titi, Global well-posedness of the 3D primitive equations with partial vertical turbulence mixing heat diffusion,, Comm. Math. Phys., 310 (2012), 537.
doi: 10.1007/s00220-011-1409-4. |
[11] |
R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables,, Ann. of Math., 103 (1976), 611.
doi: 10.2307/1970954. |
[12] |
R. R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals,, Trans. Amer. Math. Soc., 212 (1975), 315.
doi: 10.1090/S0002-9947-1975-0380244-8. |
[13] |
L. C. Evans, Partial Differential Equations,, $2^{nd}$ edition, (2010).
doi: 10.1090/gsm/019. |
[14] |
E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids,, Advances in Mathematical Fluid Mechanics, (2009).
doi: 10.1007/978-3-7643-8843-0. |
[15] |
D. M. W. Frierson, A. J. Majda and O. M. Pauluis, Large scale dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit,, Commun. Math. Sci., 2 (2004), 591.
doi: 10.4310/CMS.2004.v2.n4.a3. |
[16] |
A. E. Gill, Some simple solutions for heat-induced tropical circulation,, Quart. J. Roy. Meteor. Soc., 106 (1980), 447.
doi: 10.1002/qj.49710644905. |
[17] |
G. M. Kobelkov, Existence of a solution in the large for the 3D large-scale ocean dynamics equations,, C. R. Math. Acad. Sci. Paris, 343 (2006), 283.
doi: 10.1016/j.crma.2006.04.020. |
[18] |
I. Kukavica and M. Ziane, The regularity of solutions of the primitive equations of the ocean in space dimension three,, C. R. Math. Acad. Sci. Paris, 345 (2007), 257.
doi: 10.1016/j.crma.2007.07.025. |
[19] |
I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean,, Nonlinearity, 20 (2007), 2739.
doi: 10.1088/0951-7715/20/12/001. |
[20] |
A. Larios, E. Lunasin and E. S. Titi, Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion,, J. Differential Equations, 255 (2013), 2636.
doi: 10.1016/j.jde.2013.07.011. |
[21] |
J. Li and E. S. Titi, Global well-posedness of the 2D Boussinesq equations with vertical dissipation,, Arch. Ration. Mech. Anal., 220 (2016), 983.
doi: 10.1007/s00205-015-0946-y. |
[22] |
J. Li, E. S. Titi and Z. Xin, On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in $\mathbb R^2$,, Math. Models Methods Appl. Sci., 26 (2016), 803.
doi: 10.1142/S0218202516500184. |
[23] |
J. L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications,, Nonlinearity, 5 (1992), 237.
doi: 10.1088/0951-7715/5/2/001. |
[24] |
J. L. Lions, R. Temam and S. Wang, On the equations of the large-scale ocean,, Nonlinearity, 5 (1992), 1007.
doi: 10.1088/0951-7715/5/5/002. |
[25] |
J. L. Lions, R. Temam and S. Wang, Mathematical theory for the coupled atmosphere-ocean models (CAO III),, J. Math. Pures Appl., 74 (1995), 105.
|
[26] |
A. J. Majda and J. A. Biello, The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves,, J. Atmos. Sci., 60 (2003), 1809.
doi: 10.1175/1520-0469(2003)060<1809:TNIOBA>2.0.CO;2. |
[27] |
T. Matsuno, Quasi-geostrophic motions in the equatorial area,, J. Meteor. Soc. Japan, 44 (1966), 25. Google Scholar |
[28] |
T. K. Wong, Blowup of solutions of the hydrostatic Euler equations,, Proc. Amer. Math. Soc., 143 (2015), 1119.
doi: 10.1090/S0002-9939-2014-12243-X. |
[1] |
Xiaopeng Zhao, Yong Zhou. Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 795-813. doi: 10.3934/dcdsb.2020142 |
[2] |
Boris Andreianov, Mohamed Maliki. On classes of well-posedness for quasilinear diffusion equations in the whole space. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 505-531. doi: 10.3934/dcdss.2020361 |
[3] |
Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020382 |
[4] |
Dongfen Bian, Yao Xiao. Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1243-1272. doi: 10.3934/dcdsb.2020161 |
[5] |
Noufel Frikha, Valentin Konakov, Stéphane Menozzi. Well-posedness of some non-linear stable driven SDEs. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 849-898. doi: 10.3934/dcds.2020302 |
[6] |
Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248 |
[7] |
Tong Tang, Jianzhu Sun. Local well-posedness for the density-dependent incompressible magneto-micropolar system with vacuum. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020377 |
[8] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[9] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[10] |
Yi Guan, Michal Fečkan, Jinrong Wang. Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1157-1176. doi: 10.3934/dcds.2020313 |
[11] |
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021015 |
[12] |
Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020398 |
[13] |
Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331 |
[14] |
Hui Zhao, Zhengrong Liu, Yiren Chen. Global dynamics of a chemotaxis model with signal-dependent diffusion and sensitivity. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021011 |
[15] |
Shujing Shi, Jicai Huang, Yang Kuang. Global dynamics in a tumor-immune model with an immune checkpoint inhibitor. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1149-1170. doi: 10.3934/dcdsb.2020157 |
[16] |
Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 |
[17] |
Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020348 |
[18] |
Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh. Asymptotic dynamics of hermitian Riccati difference equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020365 |
[19] |
Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296 |
[20] |
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 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]