Small $\dot B^{-1}_{\infty,\infty}$ implies regularity
Taoufik Hmidi, Dong Li
Abstract
We show that smallness of $\dot B^{-1}_{\infty,\infty}$ norm of solution to $d$-dimensional ($d\ge 3$) incompressible Navier-Stokes prevents blowups.
Table of Contents
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Small $\dot B^{-1}_{\infty,\infty}$ implies regularity
Authors
Taoufik Hmidi, Dong Li
Abstract
We show that smallness of norm of solution to -dimensional () incompressible Navier-Stokes prevents blowups.
Paper Structure
This paper contains 2 sections, 3 theorems, 16 equations.
Table of Contents
Key Result
Theorem 1.1
Let $d\ge 3$. Suppose $v$ is a smooth solution to e1 and let $T>0$ be the first possible blow-up time. There exists a positive constant $m_0$ depending only on the dimension $d$, such that if the solution $v$ satisfies for some $0 < \epsilon <T$, then $T$ is not a blow-up time, and the solution can be continued past $T$.
Theorems & Definitions (7)
- Theorem 1.1
- Remark 1.2
- Lemma 2.1
- proof : Proof of Lemma \ref{['lem1']}
- Lemma 2.2
- proof : Proof of Lemma \ref{['lem2']}
- proof : Proof of Theorem \ref{['thm1']}