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arXiv · 1603.08301

Global well-posedness for the 2D Boussinesq Equations with Zero Viscosity

Daoguo Zhou·Zilai Li
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Abstract

We prove the global well-posedness of the two-dimensional Boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data [ $u_{0}\in L^{2}$, $\text{curl}\,u_{0}\in L^{\infty}$ and $\theta_{0}\in B^{2-2/p}_{q,p}$ with $p\in (1,\infty)$, $q\in (2,\infty)$ ]. Our method is based on the maximal regularity for heat equation.

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Daoguo Zhou, Zilai Li. 2016-03-28. Global well-posedness for the 2D Boussinesq Equations with Zero Viscosity. https://doi.org/10.1016/j.jmaa.2016.10.058

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