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math.AP2018
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…
math.AP2018
Existence theory for non-separable mean field games in Sobolev spaces
David M. Ambrose
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity.…
math.AP2018
Confinement of vorticity for the 2D Euler-alpha equations
David Ambrose, Milton Lopes Filho, Helena Nussenzveig Lopes
In this article we consider weak solutions of the Euler- equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bo…