Finite time blow up for a Navier-Stokes like equation

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Finite time blow up for a Navier-Stokes like equation

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/9695

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Title: Finite time blow up for a Navier-Stokes like equation
Author: Montgomery-Smith, Stephen, 1963-
Keywords: Cheap Navier-Stokes equation
Semigroup method
Date: 2011-01-25
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.
URI: http://hdl.handle.net/10355/9695

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