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arXiv · 1710.04860

Analyticity of solutions to the primitive equations

Yoshikazu Giga·Mathis Gries·Matthias Hieber·Amru Hussein·Takahito Kashiwabara
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Abstract

This article presents the maximal regularity approach to the primitive equations. It is proved that the $3D$ primitive equations on cylindrical domains admit a unique, global strong solution for initial data lying in the critical solonoidal Besov space $B^{2/p}_{pq}$ for $p,q\in (1,\infty)$ with $1/p+1/q \leq 1$. This solution regularize instantaneously and becomes even real analytic for $t>0$.

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Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein, Takahito Kashiwabara. 2017-10-13. Analyticity of solutions to the primitive equations. https://doi.org/10.1002/mana.201700401

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