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math.AP2026
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]…
math.AP2026
Invariant measures for the one-dimensional stochastic Navier-Stokes-Korteweg equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
We investigate the long-time behaviour of a one-dimensional compressible viscous fluid with general capillarity and density dependent viscosity, driven by a stochastic force. In pa…
math.AP2026
Global unique solvability of the 1D stochastic Navier-Stokes-Korteweg equations
L. Pescatore
We prove the global well-posedness of the one-dimensional Navier-Stokes-Korteweg equations driven by a stochastic multiplicative noise. The analysis is performed for the general ca…