Different boundary conditions for the Navier-Stokes equations in bounded Lipschitz domains in R 3 , such as Dirichlet, Neumann, Hodge, or Robin boundary conditions, are presented here. The situation is a little different from the case of smooth domains. The analysis of the problem involves a good comprehension of the behavior near the boundary. The linear Stokes operator associated to the various boundary conditions is first studied. Then a classical fixed-point theorem is used to show how the properties of the operator lead to local solutions or global solutions for small initial data.
|Title of host publication||Handbook of Mathematical Analysis in Mechanics of Viscous Fluids|
|Number of pages||42|
|State||Published - Apr 19 2018|
Bibliographical notePublisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
ASJC Scopus subject areas
- Mathematics (all)
- Physics and Astronomy (all)
- Engineering (all)