We investigate the long-time solvability in Besov spaces of the initial value problem for the inviscid 3D-Boussinesq equations with Coriolis force. First we prove a local existence and uniqueness result with critical and supercritical regularity and existence-time $ T $ uniform with respect to the rotation speed $ \Omega $. Afterwards, we show a blow-up criterion of BKM type, estimates for arbitrarily large $ T $, and then obtain the long-time existence and uniqueness of solutions for arbitrary initial data, provided that $ \Omega $ is large enough.

中文翻译：

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3D-Boussinesq-Coriolis方程在Besov空间中的长期可解性

对于具有科里奥利力的无粘性3D-Boussinesq方程，我们研究了Besov空间中初值问题的长时间可解性。首先，我们证明了具有临界和超临界规则性且存在时间$ T $关于转速$ \ Omega $均匀的局部存在和唯一性结果。然后，我们展示了BKM类型的分解准则，估计了任意大的$ T $，然后获得了任意初始数据的长期存在性和唯一性，前提是$ \ Omega $足够大。