Analyticity of solutions to the primitive equations

Abstract

This article presents the maximal regularity approach to the primitive equations. It is proved that the $3D$ primitive equations on cylindrical domains admit a unique, global strong solution for initial data lying in the critical solonoidal Besov space $B_{pq}^{2/p}$ for $p,q\in (1,\infty )$ with $1/p+1/q\le 1$. This solution regularize instantaneously and becomes even real analytic for $t>0$.

19 pages

References in corpus (7)

• Global Strong Well-posedness of the Three Dimensional Primitive equations in $L^p$-spaces
• Critical spaces for quasilinear parabolic evolution equations and applications
• The primitive equations of the atmosphere in presence of vapor saturation
• Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations with Heat and Salinity Diffusion
• Global well-posedness for passively transported nonlinear moisture dynamics with phase changes
• The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions
• The Primitive Equations in the scaling invariant space $L^{\infty }(L^1)$

Cited by in corpus (8)

• Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations
• The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions
• The Primitive Equations in the scaling invariant space $L^{\infty }(L^1)$
• Partial and full hyper-viscosity for Navier-Stokes and primitive equations
• The primitive equations with stochastic wind driven boundary conditions
• Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
• Interaction of geophysical flows with sea ice dynamics
• Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space $L^\infty_H L^q_{x_3}(\Torus^3)$