On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on \(L^{\infty }\)
The authors study the Boussinesq model of a viscous incompressible fluid in the \(n+1\) dimensional half space, \[ \mathbb R^{n + 1}_{+} = \{x= (\tilde{x},x_n)\in \mathbb R^{n + 1}; \tilde{x} \in \mathbb R^{n}, x_{n + 1} > 0\}. \] The local existence theorem for the Boussinesq equations with non-decaying data is established in the Besov space \(\mathbf B^\alpha_{pq}\) with the help of the continuity equation and the Dirichlet boundary conditions. The Besov space \(\mathbf B^\alpha_{pq}\) is a complete quasinormed space which is a Banach space when \(1 \leq p, q \leq \infty\). Finally, the uniqueness of the problem is proved.
scientific article; zbMATH DE number 5549447
scientific article