6 papers
Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity…
Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
In this paper we prove the global in time well-posedness of strong solutions to the Quantum-Navier-Stokes equation driven by random initial data and stochastic external force. In p…
Strong convergence of the vorticity and conservation of the energy for the -Euler equations
Stefano Abbate, Gianluca Crippa, Stefano Spirito
In this paper, we study the convergence of solutions of the -Euler equations to solutions of the Euler equations on the -dimensional torus. In particular, given an initial vo…
Renormalized solutions to the continuity equation with an integrable damping term
Maria Colombo, Gianluca Crippa, Stefano Spirito
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions proved that, when the damping term is bounded in…
Renormalized solutions of the 2d Euler equations
Gianluca Crippa, Stefano Spirito
In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.
Weak solutions of Navier-Stokes equations constructed by artificial compressibility method are suitable
D. Donatelli, S. Spirito
In this paper we prove that weak solution constructed by artificial compressibility method are suitable in the sense of Scheffer. Using Hilbertian setting and Fourier transform wit…