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Local well-posedness of the Benjamin-Ono equation with spatially quasiperiodic data
Sultan Aitzhan, David M. Ambrose
We consider the Benjamin-Ono equation in the spatially quasiperiodic setting. We establish local well-posedness of the initial value problem with initial data in quasiperiodic Sobo…
Asymptotics of two-dimensional hydroelastic waves: The zero mass, zero bending limit
Shunlian Liu, David M. Ambrose
We consider two-dimensional hydroelastic waves, in which a free fluid surface separates two fluids of infinite vertical extent. Elastic effects are accounted for at the interface,…
Kinetic-type Mean Field Games with Non-separable Local Hamiltonians
David M. Ambrose, Megan Griffin-Pickering, Alpár R. Mészáros
We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables repres…
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…
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…
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 {…