3 papers
math.AP2026
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…
math.AP2024
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…
math.AP2024
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…