The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space

2010/07/12 by Igor Kukavica, Vlad Vicol, Kukavica, Igor +1
Mathematics · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1007.2011

To appear in DCDS-A

arxiv created 2010/07/13 · arxiv updated 2010/07/14

Abstract

We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution u(t) in terms of exp∫₀^t \Vert ∇ u(s) \Vert_L^∞ ds, improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.

Related

• On the local analyticity for the Euler equations
• Analyticity estimates for the Navier-Stokes equations
• Space-time analyticity and refined analyticity radius of the Navier-Stokes equations in the critical Besov spaces
• New lower bounds on the radius of spatial analyticity for the KdV equation
• The uniform time of existence of the smooth solution for 3D Euler-α equations with Dirichlet boundary conditions