Finite time blow up for a Navier-Stokes like equation
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- by Stephen Montgomery-Smith PDF
- Proc. Amer. Math. Soc. 129 (2001), 3025-3029 Request permission
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 $\dot B^{-1,\infty }_\infty$. We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.References
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Additional Information
- Stephen Montgomery-Smith
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- Email: stephen@math.missouri.edu
- Received by editor(s): March 1, 2000
- Published electronically: April 17, 2001
- Additional Notes: The author was partially supported by NSF grant DMS 9870026.
- Communicated by: David S. Tartakoff
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3025-3029
- MSC (2000): Primary 35Q30, 46E35; Secondary 34G20, 37L05, 47D06, 47H10
- DOI: https://doi.org/10.1090/S0002-9939-01-06062-2
- MathSciNet review: 1840108