论文标题
在傅立叶类型的框架中，分层的分数Boussinesq-Coriolis系统的全球适应性度
Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type
论文作者
论文摘要
我们建立了3D分数Boussinesq-Coriolis系统的全球良好性，并在傅立叶类型的框架中进行分层，即傅立叶 - 巴索夫类型的空间，其基础空间是Morrey空间（很短）。在适当的条件和重新密度波动下，相对于科里奥利和分层参数，结果是均匀的。我们涵盖了耗散的关键案例，即半拉普拉斯，其中非局部耗散的差异与非线性相同，并且对二次非线性的缩放程度相同。作为副产品，考虑到微不足道的初始温度和无效分层，我们还获得了分数Navier-Stokes-Coriolis系统的FBM空间以及具有关键耗散的Navier-Stokes方程的良好结果。此外，由于在FBM空间的薄弱规范中采取了较小的条件，因此我们可以考虑一些具有任意大的$ H^{s} $的初始数据，$ S \ geq0 $。
We establish the global well-posedness of the 3D fractional Boussinesq-Coriolis system with stratification in a framework of Fourier type, namely spaces of Fourier-Besov type with underlying space being Morrey spaces (FBM-spaces, for short). Under suitable conditions and rescaled density fluctuation, the result is uniform with respect to the Coriolis and stratification parameters. We cover the critical case of the dissipation, namely half-Laplacian, in which the nonlocal dissipation has the same differential order as the nonlinearity and balances critically the scaling of the quadratic nonlinearities. As a byproduct, considering trivial initial temperature and null stratification, we also obtain well-posed results in FBM-spaces for the fractional Navier-Stokes-Coriolis system as well as for the Navier-Stokes equations with critical dissipation. Moreover, since small conditions are taken in the weak norm of FBM-spaces, we can consider some initial data with arbitrarily large $H^{s}$-norms, $s\geq0$.
