6 papers
Uniqueness of solutions to the 2D compressible Navier-Stokes equations for bounded densities
Lorenzo Pescatore, Alessandro Violini
We prove the uniqueness of global solutions to the two dimensional barotropic compressible Navier--Stokes equations within the regularity class introduced by Danchin and Mucha [14]…
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 Škondrić, 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 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…
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…
Relative Energy Method For Weak-Strong Uniqueness Of The Inhomogeneous Navier-Stokes Equations
Timothée Crin-Barat, Stefan Škondrić, Alessandro Violini
We present a weak-strong uniqueness result for the inhomogeneous Navier-Stokes (INS) equations in () for bounded initial densities that are far from vacuum. G…