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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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