Stokes Problems in Irregular Domains with Various Boundary Conditions

Sylvie Monniaux () and Zhongwei Shen ()
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Sylvie Monniaux: CNRS, Centrale Marseille, Aix-Marseille Université
Zhongwei Shen: University of Kentucky

Chapter 4 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 207-248 from Springer

Abstract: Abstract Different boundary conditions for the Navier-Stokes equations in bounded Lipschitz domains in ℝ 3 $$\mathbb{R}^{3}$$ , 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.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_4

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