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arXiv · 1703.09698

On singular limit equations for incompressible fluids in moving thin domains

Tatsu-Hiko Miura
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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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Tatsu-Hiko Miura. 2017-03-28. On singular limit equations for incompressible fluids in moving thin domains. https://arxiv.org/abs/1703.09698

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