Global wellposedness of the primitive equations with nonlinear equation of state in critical spaces

DOI10.1007/978-3-031-19252-4_1MaRDI QIDQ6614860

Matthias Hieber, Tim Binz

Publication date: 8 October 2024

zbMATH Keywords

primitive equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) One-parameter semigroups and linear evolution equations (47D06) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Geophysical flows (76U60)

Cites Work

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• Global strong \(L^{p}\) well-posedness of the 3D primitive equations with heat and salinity diffusion
• Addendum to the paper ``On quasilinear parabolic evolution equations in weighted \(L_p\)-spaces II
• A generalization of a theorem by Kato on Navier-Stokes equations
• Global well-posedness of the ocean primitive equations with nonlinear thermodynamics
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
• Global strong well-posedness of the three dimensional primitive equations in \({L^p}\)-spaces
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• The Theory of Large-Scale Ocean Circulation
• New formulations of the primitive equations of atmosphere and applications
• On the equations of the large-scale ocean
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces
• Analyticity of solutions to the primitive equations
• Mathematical Analysis of the Navier-Stokes Equations
• Bounded 𝐻^{∞}-calculus for the hydrostatic Stokes operator on 𝐿^{𝑝}-spaces and applications
• On the regularity of the primitive equations of the ocean

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