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14 papers · 2 filters
On the derivation of the homogeneous kinetic wave equation
Charles Collot, Pierre Germain
The nonlinear Schrödinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greate…
On self-similar solutions to degenerate compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi, Tristan Léger
We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existen…
Higher-order linearization and regularity in nonlinear homogenization
Scott Armstrong, Samuel J. Ferguson, Tuomo Kuusi
We prove large-scale regularity for solutions of nonlinear elliptic equations with random coefficients, thereby obtaining a version of the statement of Hilbert's 19th pr…
Stationary flows for compressible viscous fluid in a perturbed half-space
Masahiro Suzuki, Katherine Zhiyuan Zhang
We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been…
Stability threshold of the 2D Couette flow in Sobolev spaces
Nader Masmoudi, Weiren Zhao
We study the stability threshold of the 2D Couette flow in Sobolev spaces at high Reynolds number . We prove that if the initial vorticity satisfies $\|Ω_{in}-(-1)\|_{…
Enhanced dissipation for the 2D Couette flow in critical space
Nader Masmoudi, Weiren Zhao
We consider the 2D incompressible Navier-Stokes equations on , with initial vorticity that is close in to (the vorticity of…