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

Fuente: arXiv
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Main Authors: Donatelli, Donatella, Pescatore, Lorenzo, Spirito, Stefano
Format: Preprint
Published: 2024
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author Donatelli, Donatella
Pescatore, Lorenzo
Spirito, Stefano
author_facet Donatelli, Donatella
Pescatore, Lorenzo
Spirito, Stefano
contents 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
format Preprint
id arxiv_https___arxiv_org_abs_2412_10875
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations
Donatelli, Donatella
Pescatore, Lorenzo
Spirito, Stefano
Analysis of PDEs
35Q35, 60H15, 76M35
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
title Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations
topic Analysis of PDEs
35Q35, 60H15, 76M35
url https://arxiv.org/abs/2412.10875