The inviscid inflow-outflow problem via analyticity

2023/10/31 by Igor Kukavica, Wojciech Ożański, Kukavica, Igor +5 · 3 citations
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.2310.20439

Abstract

We consider the incompressible Euler equation on an analytic domain Ω with nonhomogeneous boundary condition u⋅ n = u ⋅ n on ∂ Ω, where u is a given divergence-free analytic vector field. We establish local well-posedness for u in analytic spaces without any compatibility conditions in all space dimensions. We also prove global well-posedness in the 2D case if u decays in time sufficiently fast.

Citations

• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Analyticity up to the boundary for the Stokes and the Navier-Stokes systems
• Analyticity up to the boundary of solutions of nonlinear parabolic equations

Cited by

• The TURBO method for well-posedness of the incompressible Euler equations in Sobolev spaces in any domain
• On the vanishing viscosity limit for incompressible flows with inflow/outflow boundary conditions
• On Vanishing Viscosity with Inflow, Outflow

Related

• On the local analyticity for the Euler equations
• Inhomogeneous incompressible Euler with codimension 1 singular structures
• Geometric blow-up criteria for the non-homogeneous incompressible Euler equations in 2-D
• The linearized 3D Euler equations with inflow, outflow
• Ill-posedness for the incompressible Euler equations in critical Sobolev spaces