### Abstract

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of first order Euler and Prandtl corrections plus a further error term. The equation for the error term is weakly nonlinear; its linear part is the time dependent Stokes equation. This error equation is solved by inversion of the Stokes equation, through expressing the solution as a regular (Euler-like) part plus a boundary layer (Prandtl-like) part. The main technical tool in this analysis is the Abstract Cauchy-Kowalewski Theorem.

Original language | English (US) |
---|---|

Pages (from-to) | 463-491 |

Number of pages | 29 |

Journal | Communications In Mathematical Physics |

Volume | 192 |

Issue number | 2 |

DOIs | |

State | Published - 1998 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Zero viscosity limit for analytic solutions of the navier-stokes equation on a half-space. II. Construction of the Navier-stokes solution'. Together they form a unique fingerprint.

## Cite this

*Communications In Mathematical Physics*,

*192*(2), 463-491. https://doi.org/10.1007/s002200050305