Finite time blow up for a Navier-Stokes like equation

1999/11/30 by Stephen Montgomery-Smith · 2 citations
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.CA #math.FA #math.MP #msc:35Q30 #msc:46E35 #msc:34G20 #msc:37L05 #msc:47D06 #msc:47H10

paper · pdf

published as Proc. A.M.S., 129, (2001), 3017-3023 · Also available at http://www.math.missouri.edu/~stephen/preprints/

arxiv created 2000/07/10 · arxiv updated 2009/11/30

Abstract

We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space B^-1,∞_∞. We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.

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