Global well-posedness of strong solutions to the primitive equations without vertical diffusivity

DOI10.1016/j.aml.2023.108943MaRDI QIDQ6202724

Xue-ke Pu, Wenli Zhou

Publication date: 27 February 2024

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

strong solutionswell-posednessprimitive equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Stratification effects in inviscid fluids (76B70) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Geophysical flows (76U60)

Cites Work

• Strong solutions to the 3D primitive equations with only horizontal dissipation: near \(H^{1}\) initial data
• Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity
• The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation
• The hydrostatic Stokes semigroup and well-posedness of the primitive equations on spaces of bounded functions
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
• Existence of a solution `in the large' for the 3D large-scale ocean dynamics equations
• Global strong well-posedness of the three dimensional primitive equations in \({L^p}\)-spaces
• The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations
• Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation
• New formulations of the primitive equations of atmosphere and applications
• On the equations of the large-scale ocean
• Global well-posedness of z-weak solutions to the primitive equations without vertical diffusivity
• On the regularity of the primitive equations of the ocean
• On the rigorous mathematical derivation for the viscous primitive equations with density stratification
• Global existence and asymptotic stability of the free boundary problem of the primitive equations with heat insulation

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