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arXiv · 1512.00898

Very weak solutions of the Stokes problem in a convex polygon

Makram Hamouda·Roger Temam·Le Zhang
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Abstract

Motivated by the study of the corner singularities in the so-called cavity flow, we establish in this article, the existence and uniqueness of solutions in $L^2(\Omega)^2$ for the Stokes problem in a domain $\Omega,$ when $\Omega$ is a smooth domain or a convex polygon. We establish also a trace theorem and show that the trace of $u$ can be arbitrary in $L^2(\partial\Omega)^2.$ The results are also extended to the linear evolution Stokes problem.

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Makram Hamouda, Roger Temam, Le Zhang. 2015-12-02. Very weak solutions of the Stokes problem in a convex polygon. https://arxiv.org/abs/1512.00898

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