10 papers · 1 filter
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…
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…
Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction
David M. Ambrose, Anna L. Mazzucato
In two spatial dimensions, there are very few global existence results for the Kuramoto-Sivashinsky equation. The majority of the few results in the literature are strongly anisotr…
Well-posedness and asymptotics of a coordinate-free model of flame fronts
David M. Ambrose, Fazel Hadadifard, J. Douglas Wright
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter which relates to how unstable the front might be. We fi…
Existence theory for a time-dependent mean field games model of household wealth
David M. Ambrose
We study a nonlinear system of partial differential equations arising in macroeconomics which utilizes a mean field approximation. This system together with the corresponding data,…
Well-posedness of fully nonlinear KdV-type evolution equations
Timur Akhunov, David M. Ambrose, J. Douglas Wright
We study the well-posedness of the initial value problem for fully nonlinear evolution equations, where may depend on up to the first three spatial derivatives of…