43 citations · 99 across the 23 of their papers we have counts for
26 papers
Existence and analyticity of solutions of the Kuramoto-Sivashinsky equation with singular data
David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any sp…
Contour dynamics and global regularity for periodic vortex patches and layers
David M. Ambrose, Fazel Hadadifard, James P. Kelliher
We study vortex patches for the 2D incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We…
Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains
David M. Ambrose, Pavel M. Lushnikov, Michael Siegel +1
The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation , where $\widehat {…
Existence of Solutions to Fluid Equations in Hölder and Uniformly Local Sobolev Spaces
David M. Ambrose, Elaine Cozzi, Daniel Erickson +1
We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the Hölder spaces for and the uniformly local Sobolev spa…
Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus
D. M. Ambrose, M. C. Lopes Filho, H. J. Nussenzveig Lopes
Lei and Lin have recently given a proof of a global mild solution of the three-dimensional Navier-Stokes equations in function spaces based on the Wiener algebra. An alternative pr…
Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels
Hyeju Kim, David M. Ambrose
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial directio…