4 papers
Well-Posedness and Logarithmic Lipschitz Regularity for the Density Patch Problem
Alessandro Violini
We study the density patch problem for the two-dimensional inhomogeneous incompressible Navier--Stokes system with vacuum, for initial data consisting of a Lipschitz density patch…
On Lions' density patch problem at a critical level of regularity
Stefan Å kondriÄ, Alessandro Violini
In this article, we study Lions' density patch problem in two space dimensions at critical regularity. We prove global existence, uniqueness, and stability for a fluid occupying a…
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 Å kondriÄ +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…
Inhomogeneous incompressible Euler with codimension singular structures
Marco Inversi, Alessandro Violini
This paper is concerned with the inhomogeneous incompressible Euler system. We establish a Duchon--Robert type approximation theorem for the distribution describing the local energ…