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Local well-posedness and a blow up criterion for the inviscid Boussinesq system in Hölder spaces. (English) Zbl 1274.35280
Summary: We prove the local well-posedness and a blow up criterion of solutions in the Hölder spaces for the inviscid Bounssinesq system in \(\mathbb{R}^N,\;N\geq 2\), under the assumptions that the initial values \(\theta_0,u_0\in C^r\) with \(1<r\neq 2\).

MSC:
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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