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arXiv · 1203.1129

New maximal regularity results for the heat equation in exterior domains, and applications

Raphaël Danchin·Piotr B. Mucha
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Abstract

This paper is dedicated to the proof of new maximal regularity results involving Besov spaces for the heat equation in the half-space or in bounded or exterior domains of R^n. We strive for time independent a priori estimates in regularity spaces of type L^1(0,T;X) where X stands for some homogeneous Besov space. In the case of bounded domains, the results that we get are similar to those of the whole space or of the half-space. For exterior domains, we need to use mixed Besov norms in order to get a control on the low frequencies. Those estimates are crucial for proving global-in-time results for nonlinear heat equations in a critical functional framework.

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Raphaël Danchin, Piotr B. Mucha. 2012-03-06. New maximal regularity results for the heat equation in exterior domains, and applications. https://arxiv.org/abs/1203.1129

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