Existence of Solutions to Fluid Equations in Hölder and Uniformly Local Sobolev Spaces

2022/06/13 by David M. Ambrose, Ambrose, David M., Elaine Cozzi +5 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2206.05861

openalex publication_date 2022/06/13 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

Abstract

We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the Hölder spaces C^r(ℝ²) for r>1 and the uniformly local Sobolev spaces H^s_ul(ℝ²) for s≥ 3. Using methods similar to those for the surface quasi-geostrophic equation, we also obtain short-time existence for the three-dimensional Euler equations in uniformly local Sobolev spaces.

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