On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions

DOI10.1137/140956440zbMATH Open1317.35202arXiv1402.1984OpenAlexW2091516904MaRDI QIDQ5179163

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Publication date: 19 March 2015

Published in: (Search for Journal in Brave)

Abstract: We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, we assume that the initial datum

u_{0}

is monotone on a number of intervals (on some strictly increasing on some strictly decreasing) and analytic on the complement and show that the local existence and uniqueness hold. The same is true for the hydrostatic Euler equations except that we assume this for the vorticity

o m e g a_{0} = p a r t i a l_{y} u_{0}

.

Full work available at URL: https://arxiv.org/abs/1402.1984

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