On singular limit equations for incompressible fluids in moving thin domains

Miura, Tatsu-Hiko

doi:10.1090/qam/1495

Author: Tatsu-Hiko Miura
Journal: Quart. Appl. Math. 76 (2018), 215-251
MSC (2010): Primary 35Q35, 35R01, 76M45; Secondary 76A20
DOI: https://doi.org/10.1090/qam/1495
Published electronically: December 8, 2017
MathSciNet review: 3769895
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Abstract: We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin domain goes to zero, we give a heuristic derivation of singular limit equations on the degenerate moving surface of the Euler and Navier-Stokes equations in the moving thin domain and investigate relations between their energy structures. We also compare the limit equations with the Euler and Navier-Stokes equations on a stationary manifold, which are described in terms of the Levi-Civita connection.

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