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math.AP2001
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
Stephen Montgomery-Smith, Milan Pokorny
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper…
math.AP1999
Finite time blow up for a Navier-Stokes like equation
Stephen Montgomery-Smith
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…
math.AP1998
Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions
Stephen J. Montgomery-Smith
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes e…