A Solvability criterion for Navier-Stokes equations in high dimensions

Details A Solvability criterion for Navier-Stokes equations in high dimensions A Solvability criterion for Navier-Stokes equations in high dimensions

2009-07-24

arxiv.org/abs/0907.4357v2

Mathematics

Analysis of PDEs

Fixed references, priority etc

Scientific paper

We define the Ladyzhenskaya-Lions exponent $\alpha_{\rm {\tiny \sc l}} (n)=({2+n})/4$ for Navier-Stokes equations with dissipation $-(-\Delta)^{\alpha}$ in ${\Bbb R}^n$, for all $n\geq 2$. We review the proof of strong global solvability when $\alpha\geq \alpha_{\rm {\tiny \sc l}} (n)$, given smooth initial data. If the corresponding Euler equations for $n>2$ were to allow uncontrolled growth of the enstrophy ${1\over 2} \|\nabla u \|^2_{L^2}$, then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for $\alpha<\alpha_{\rm {\tiny \sc l}} (n)$. The energy is critical under scale transformations only for $\alpha=\alpha_{\rm {\tiny \sc l}} (n)$.

Affiliated with

Also associated with

No associations

Rating

A Solvability criterion for Navier-Stokes equations in high dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Solvability criterion for Navier-Stokes equations in high dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Solvability criterion for Navier-Stokes equations in high dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310860