### 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, if 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 of these intervals, we show that the local existence and uniqueness hold. The same result is true for the hydrostatic Euler equations if we assume these conditions for the initial vorticity ω_{0} = ∂_{y}u0.

Original language | English (US) |
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Pages (from-to) | 3865-3890 |

Number of pages | 26 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 46 |

Issue number | 6 |

DOIs | |

State | Published - 2014 |

### Keywords

- Boundary layer
- Euler equations
- Hydrostatic balance
- Inviscid limit
- Navier-Stokes equations
- Prandtl equations

### ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'On the local well-posedness of the prandtl and hydrostatic euler equations with multiple monotonicity regions'. Together they form a unique fingerprint.

## Cite this

Kukavica, I., Masmoudi, N., Vicol, V., & Wong, T. K. (2014). On the local well-posedness of the prandtl and hydrostatic euler equations with multiple monotonicity regions.

*SIAM Journal on Mathematical Analysis*,*46*(6), 3865-3890. https://doi.org/10.1137/140956440