Stokes Problems in Irregular Domains with Various Boundary Conditions

Sylvie Monniaux (1) , Zongwei Shen (2)

1 I2M - Institut de Mathématiques de Marseille
2 University of Kentucky

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 behaviour 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.

Domaines: Equations aux dérivées partielles [math.AP]

Sylvie Monniaux, Zongwei Shen. Stokes Problems in Irregular Domains with Various Boundary Conditions. Yoshikazu Giga, Antonin Novotny Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 59, Springer, pp.1-42, 2016, 978-3-319-10151-4. ⟨10.1007/978-3-319-10151-4_4-1⟩. ⟨hal-01481981⟩