Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations

2024/12/14 by Donatella Donatelli, Donatelli, Donatella, Lorenzo Pescatore +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Navier-Stokes equation solutions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.10875

Abstract

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, driven by random initial data and a stochastic forcing term. These solutions are weak in both PDEs and Probability sense and may have vacuum regions. The proof relies on the construction of an approximating system which provides extra dissipation properties and the convergence is based on an appropriate truncation of the velocity field in the momentum equation and a stochastic compactness argument

Cited by

• Global Weak Solutions for the High--Friction Quantum Navier--Stokes--Poisson Model

Related

• The Global Existence of Martingale Solutions to Stochastic Compressible Navier-Stokes Equations with Density-dependent Viscosity
• Random Perturbations of Viscous Compressible Fluids: Global Existence of Weak Solutions
• Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit
• Sequential stability of weak martingale solutions to stochastic compressible Navier-Stokes equations with viscosity vanishing on vacuum
• Existence of martingale solutions and the incompressible limit for stochastic compressible flows on the whole space