### Abstract

We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear 2 1/2-dimensional limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.

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

Pages (from-to) | 51-57 |

Number of pages | 7 |

Journal | Applied Mathematics Letters |

Volume | 13 |

Issue number | 4 |

State | Published - May 2000 |

### Fingerprint

### Keywords

- Resonances
- Rotation
- Three-dimensional Navier-Strokes equations

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Applied Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics Letters*,

*13*(4), 51-57.

**Global regularity of 3D rotating Navier-Stokes equations for resonant domains.** / Babin, A.; Mahalov, Alex; Nicolaenko, B.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 13, no. 4, pp. 51-57.

}

TY - JOUR

T1 - Global regularity of 3D rotating Navier-Stokes equations for resonant domains

AU - Babin, A.

AU - Mahalov, Alex

AU - Nicolaenko, B.

PY - 2000/5

Y1 - 2000/5

N2 - We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear 2 1/2-dimensional limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.

AB - We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear 2 1/2-dimensional limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.

KW - Resonances

KW - Rotation

KW - Three-dimensional Navier-Strokes equations

UR - http://www.scopus.com/inward/record.url?scp=0039247150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039247150&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039247150

VL - 13

SP - 51

EP - 57

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 4

ER -