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

Zachary Bradshaw; Tai-Peng Tsai

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arXiv · 2008.09204

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

Zachary Bradshaw·Tai-Peng Tsai

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Abstract

We establish existence of solutions in a scale of classes weaker than the finite energy Leray class and stronger than the infinite energy Lemari\'e-Rieusset class. The new classes are based on the $L^2$ Wiener amalgam spaces. Solutions in the classes closer to the Leray class are shown to satisfy some properties known in the Leray class but not the Lemari\'e-Rieusset class, namely eventual regularity and long time estimates on the growth of the local energy. In this sense, these solutions bridge the gap between Leray's original solutions and Lemari\'e-Rieusset's solutions and help identify scalings at which certain properties may break down.

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Zachary Bradshaw, Tai-Peng Tsai. 2020-08-20. Local energy solutions to the Navier-Stokes equations in Wiener amalgam spaces. https://arxiv.org/abs/2008.09204

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