### Abstract

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x_{2} = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

Original language | English (US) |
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Pages (from-to) | 1932-1946 |

Number of pages | 15 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 49 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Keywords

- Euler equations
- Inviscid limit
- Navier-Stokes equations

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## Cite this

Constantin, P., Elgindi, T., Ignatova, M., & Vicol, V. (2017). Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields.

*SIAM Journal on Mathematical Analysis*,*49*(3), 1932-1946. https://doi.org/10.1137/15M1054572