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math.AP2024
Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus
David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
We consider the three-dimensional Navier-Stokes equations, with initial data having second derivatives in the space of pseudomeasures. Solutions of this system with such data have…
physics.flu-dyn2024
The velocity field and Birkhoff-Rott integral for non-decaying, non-periodic vortex sheets
David M. Ambrose
The Birkhoff-Rott integral expresses the fluid velocity on a vortex sheet. This integral converges if certain quantities decay at horizontal infinity, but can also be summed over p…