Global existence and large time behavior for primitive equations with free boundary

2022/10/18 by Hai-Liang Li, Li, Hai-Liang, Chuangchuang Liang +1 · 2 citations
Mathematics · Medicine · #35A01 #35Q30 #35Q35 #35R35 #76E20 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2210.09632

openalex publication_date 2022/10/18 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

Abstract

In the present paper, the primitive equations, which can be used to simulate the large scale motion of ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary. The global existence and uniqueness of strong solutions are established and the long time convergence to the equilibrium state is showed either at exponential rate for horizontal periodic domain or at algebraic rate for horizontal whole space.

Cited by

• A geophysical free-boundary system modeling an ice-sheet interacting with an ocean
• Energy Conservation and Vanishing Viscosity Limit for the Primitive Equations

Related

• Global Well--posedness of the Three-dimensional Viscous Primitive Equations of Large Scale Ocean and Atmosphere Dynamics
• Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics
• Global attractor of the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain
• Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Horizontal Eddy Diffusivity
• Strong solutions to the 3D primitive equations with only horizontal dissipation: near H¹ initial data