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

@article{Kukavica2014OnTL,
title={On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions},
author={Igor Kukavica and Nader Masmoudi and Vlad Vicol and Tak Kwong Wong},
journal={SIAM J. Math. Analysis},
year={2014},
volume={46},
pages={3865-3890}
}
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… CONTINUE READING

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