Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
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DOI：
10.1002/cpa.21595
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发表时间：
2012-06
影响因子：
3
通讯作者：
N. Masmoudi;T. Wong
中科院分区：
文献类型：
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作者：
N. Masmoudi;T. Wong
在Oleinik单调性假设下，证明了加权Sobolev空间中二维Prandtl系统的局部存在唯一性。特别是，我们不使用Crocco变换或任何变量的变化。我们的证明是基于普朗特系统的一种新的非线性能量估计。这种新的能量估计是基于在单调性假设下有效的消去性质。为了构造解，我们使用系统的正则化来保持这种非线性结构。这种新的非线性结构可以帮助我们了解黏度趋于0时从Navier - Stokes系统到Euler系统的收敛特性。©2015 Wiley期刊公司
We prove local existence and uniqueness for the two‐dimensional Prandtl system in weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not use the Crocco transform or any change of variables. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property that 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 into the convergence properties from the Navier‐Stokes system to the Euler system when the viscosity goes to 0. © 2015 Wiley Periodicals, Inc.