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7 papers · 2 filters
On the Weak Coupling Limit of Quantum Many-body Dynamics and the Quantum Boltzmann Equation
Xuwen Chen, Yan Guo
The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam t…
Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate
Yan Guo, Toan T. Nguyen
This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosit…
Global bifurcation of steady gravity water waves with critical layers
Adrian Constantin, Walter Strauss, Eugen Varvaruca
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert…
On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
Xuwen Chen, Paul Smith
In this article we establish the unconditional uniqueness of solutions to an Infinite Radial Chern-Simons-Schrödinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarc…
Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation
Lei Wu, Yan Guo
We revisit the diffusive limit of a steady neutron transport equation in a -D unit disk with one-speed velocity. We show the classical result in [4] with Milne expansion is inco…
On a multi-dimensional transport equation with nonlocal velocity
Hongjie Dong
We study a multi-dimensional nonlocal active scalar equation of the form in , where with .…