Abstract
There is a substantial literature on the existence of solutions to the Euler and Navier-Stokes equations for incompressible flows in bounded domains Most papers concentrate on the case of domains with fairly smooth boundary, typically at least C 1,1regular. However, it is natural to consider fluid flows in rougher domains. Our discussion here has two parts. In Part I we consider the Navier-Stokes equations on Lipschitz domains in ℝ2and ℝ3 .In Part II we consider the Euler equations in a more restricted class of nonsmooth domains in the plane.
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Taylor, M.E. (2000). Incompressible Fluid Flows on Rough Domains. In: Balakrishnan, A.V. (eds) Semigroups of Operators: Theory and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 42. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8417-4_32
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DOI: https://doi.org/10.1007/978-3-0348-8417-4_32
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