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14 papers · 2 filters
Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness
Timothée Crin-Barat, Nicola De Nitti, Stefan Škondrić +1
We characterize the Leray--Hopf solutions of the 2D inhomogeneous Navier--Stokes system that become strong for positive times. This characterization relies on the strong energy ine…
Smoluchowski Coagulation Equation with a Flux of Dust Particles
Marina A. Ferreira, Aleksis Vuoksenmaa
We construct a time-dependent solution to the Smoluchowski coagulation equation with a constant flux of dust particles entering through the boundary at zero. The dust is instantane…
Isoperimetric and geometric inequalities in quantitative form: Stein's method approach
Jordan Serres
We adapt Stein's method to isoperimetric and geometric inequalities. The main challenge is the treatment of boundary terms. We address this by using an elliptic PDE with an oblique…
Ground states on a fractured strip and one dimensional reduction
Stefan Le Coz, Boris Shakarov
We consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the -axis. First, we show the existence of ground states a…
Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme
Jean-François Coulombel, Grégory Faye
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first cl…
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
Michał Borowski, Pierre Bousquet, Iwona Chlebicka +2
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Ω…