Local energy solutions to the Navier-Stokes equations in Wiener amalgam\n spaces

2020/08/20 by Zachary Bradshaw, Tai‐Peng Tsai, Bradshaw, Zachary +1
Engineering · Mathematics · #35Q30 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2008.09204

openalex publication_date 2020/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish existence of solutions in a scale of classes weaker than the\nfinite energy Leray class and stronger than the infinite energy\nLemari 'e-Rieusset class. The new classes are based on the L² Wiener amalgam\nspaces. Solutions in the classes closer to the Leray class are shown to satisfy\nsome properties known in the Leray class but not the Lemari 'e-Rieusset class,\nnamely eventual regularity and long time estimates on the growth of the local\nenergy. In this sense, these solutions bridge the gap between Leray's original\nsolutions and Lemari 'e-Rieusset's solutions and help identify scalings at\nwhich certain properties may break down.\n

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