Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface
The author proves the local existence theorem for incompressible fluid flow under the condition that both the fixed bottom and free surface of fluid tend to constants at infinity. The study uses the complicated technique of Sobolev-Slobodeskij spaces and is based on the decomposition of the solution into the sum of solutions of a linear system and a nonlinear perturbation. Global existence theorem for the linear system uses actively Solonnikov's results, whereas the local existence theorem for the nonlinear perturbation problem is proved by the method of successive approximations.
scientific article; zbMATH DE number 911920
scientific article