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29 March 2024
 
  » arxiv » math.AP/9911223

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Finite time blow up for a Navier-Stokes like equation
Stephen Montgomery-Smith ;
Date 29 Nov 1999
Journal Proc. A.M.S., 129, (2001), 3017-3023
Subject Analysis of PDEs; Classical Analysis and ODEs; Functional Analysis; Mathematical Physics MSC-class: 35Q30 46E35 (Primary); 34G20, 37L05, 47D06, 47H10 (Secondary) | math.AP math-ph math.CA math.FA math.MP
AbstractWe 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 $dot B^{-1,infty}_infty$. We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.
Source arXiv, math.AP/9911223
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