In this paper we consider the incompressible Navier-Stokes equations with a density-dependent viscosity in a bounded domain of R n (n = 2, 3). We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary f
Uniqueness for the Navier–Stokes equations and multipliers between Sobolev spaces
✍ Scribed by Pierre Gilles Lemarié-Rieusset; Ramzi May
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 284 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
✦ Synopsis
We re-prove various uniqueness theorems for the Navier-Stokes equations, stating the assumptions in terms of multipliers between Sobolev spaces instead of Lebesgue or Lorentz spaces.
📜 SIMILAR VOLUMES
## Communicated by M. Costabel In this work, we improved the regularity criterion on the Cauchy problem for the Navier-Stokes equations in multiplier space in terms of the two partial derivatives of velocity fields, @ 1 u 1 and @ 2 u 2 .
## Abstract We shall show that every strong solution __u__(__t__) of the Navier‐Stokes equations on (0, __T__) can be continued beyond __t__ > __T__ provided __u__ ∈ $L^{{{2} \over {1 - \alpha}}}$ (0, __T__; $\dot F^{- \alpha}\_{\infty ,\infty}$ for 0 < α < 1, where $\dot F^{s}\_{p,q}$ denotes the