Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
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Publication:2949771
DOI10.1002/CPA.21595zbMATH Open1326.35279arXiv1206.3629OpenAlexW1870863896MaRDI QIDQ2949771
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Publication date: 2 October 2015
Published in: (Search for Journal in Brave)
Abstract: We prove local existence and uniqueness for the two-dimensional Prandtl system in weighted Sobolev spaces under the Oleinik's monotonicity assumption. In particular we do not use the Crocco transform. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property which is valid under the monotonicity assumption. To construct the solution, we use a regularization of the system that preserves this nonlinear structure. This new nonlinear structure may give some insight on the convergence properties from Navier-Stokes system to Euler system when the viscosity goes to zero.
Full work available at URL: https://arxiv.org/abs/1206.3629
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