𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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


Unique solvability for the density-depen
✍ Yonggeun Cho; Hyunseok Kim 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 304 KB

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

On the regularity criterion for the solu
✍ Zaihong Jiang; Sadek Gala; Lidiao Ni 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 109 KB 👁 1 views

## 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 .

Bilinear estimates in homogeneous Triebe
✍ Hideo Kozono; Yukihiro Shimada 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB

## 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