Global strong well-posedness of the three dimensional primitive equations in \({L^p}\)-spaces

DOI10.1007/s00205-016-0979-xzbMath1350.35155arXiv1509.01151OpenAlexW2242847336MaRDI QIDQ2630263

Takahito Kashiwabara, Matthias Hieber

Publication date: 26 July 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01151

zbMATH Keywords

global strong solutionStokes operatorprimitive equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Meteorology and atmospheric physics (86A10) Strong solutions to PDEs (35D35)

Related Items (43)

Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations ⋮ Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity ⋮ Global wellposedness of the primitive equations with nonlinear equation of state in critical spaces ⋮ Global well-posedness of z-weak solutions to the primitive equations without vertical diffusivity ⋮ On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equations ⋮ Global strong \(L^{p}\) well-posedness of the 3D primitive equations with heat and salinity diffusion ⋮ On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations-rigorous justification ⋮ The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations ⋮ Partial and full hyper-viscosity for Navier-Stokes and primitive equations ⋮ The hydrostatic Stokes semigroup and well-posedness of the primitive equations on spaces of bounded functions ⋮ On the well-posedness of reduced \(3D\) primitive geostrophic adjustment model with weak dissipation ⋮ Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces ⋮ Large and moderate deviations principles and central limit theorem for the stochastic 3D primitive equations with gradient-dependent noise ⋮ Local martingale solutions and pathwise uniqueness for the three-dimensional stochastic inviscid primitive equations ⋮ Existence and Uniqueness of Weak Solutions to Viscous Primitive Equations for a Certain Class of Discontinuous Initial Data ⋮ Higher-order error estimates for physics-informed neural networks approximating the primitive equations ⋮ On energy conservation for the hydrostatic Euler equations: an Onsager conjecture ⋮ Data assimilation to the primitive equations with \(L^p\)-\(L^q\)-based maximal regularity approach ⋮ On the rigorous mathematical derivation for the viscous primitive equations with density stratification ⋮ Stochastic primitive equations with horizontal viscosity and diffusivity ⋮ On symmetry breaking for the Navier-Stokes equations ⋮ The primitive equations with stochastic wind driven boundary conditions ⋮ Global well-posedness of strong solutions to the primitive equations without vertical diffusivity ⋮ Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation ⋮ Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations* ⋮ Analysis of Viscous Fluid Flows: An Approach by Evolution Equations ⋮ The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation ⋮ Uniqueness of some weak solutions for 2D viscous primitive equations ⋮ Strong solutions to the 3D primitive equations with only horizontal dissipation: near \(H^{1}\) initial data ⋮ On the finite element approximation for non-stationary saddle-point problems ⋮ Finite-time blowup and ill-posedness in Sobolev spaces of the inviscid primitive equations with rotation ⋮ Strong solvability of a variational data assimilation problem for the primitive equations of large-scale atmosphere and Ocean dynamics ⋮ Primitive equations with horizontal viscosity: the initial value and the time-periodic problem for physical boundary conditions ⋮ Local well-posedness of strong solutions to the three-dimensional compressible primitive equations ⋮ Global well-posedness for the 3D primitive equations in anisotropic framework ⋮ Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise ⋮ Preface ⋮ Global well-posedness of the ocean primitive equations with nonlinear thermodynamics ⋮ The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition ⋮ The primitive equations in the scaling-invariant space \(L^{\infty}(L^1)\) ⋮ Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities ⋮ On the effect of rotation on the life-span of analytic solutions to the \(3D\) Inviscid primitive equations ⋮ Bounded 𝐻^{∞}-calculus for the hydrostatic Stokes operator on 𝐿^{𝑝}-spaces and applications

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