具有Dirichlet信号边界的趋化Navier-Stokes模型的整体适定性OA

The global well-posedness of a chemotaxis Navier-Stokes system involving quadratic decay and Dirichlet boundary conditions for the signal in a 2D bounded domain with smooth boundary is studied.To overcome the challenges posed by the non-homogeneous Dirichlet boundary conditions,the original problem is firstly transformed into the homogeneous Dirichlet boundary problem.Then,exploiting the local existence theory of solutions and the energy estimates,the global existence of uniformly bounded classical solutions is established for any suitably regular initial data.Moreover,the large-time behavior of the solution under certain additional assumptions is obtained via the Hölder estimates and the space-time estimates of solutions.