Compressible Euler equations with transport noise

2025/11/25 by Boadi, Richard, Breit, Dominic, Moyo, Thamsanqa Castern
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.20131

Abstract

We study the isentropic compressible Euler equations in multi-dimensions with stochastic perturbation of transport type. On the one hand, this is motivated by the physical modelling in turbulence theory. On the other hand, it has been shown recently that this type of noise can have regularising effects. In this paper, we prove the existence of dissipative measure-valued martingale solutions, the weak-strong uniqueness property and the existence of Markov selections.

Citations

• Compressible fluids excited by space-dependent transport noise
• Dissipative solutions and Markov selection to the complete stochastic Euler system
• Compressible Navier--Stokes system with transport noise
• Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits
• On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
• Formation of shocks for 2D isentropic compressible Euler
• Generalized solutions to models of inviscid fluids
• Markov selection for the stochastic compressible Navier--Stokes system
• Stochastic compressible Euler equations and inviscid limits
• Stochastic isentropic Euler equations
• Weak-strong uniqueness for measure-valued solutions
• Markov selections for the 3D stochastic Navier-Stokes equations

Related

• Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits
• Statistically stationary solutions to the stochastic isentropic compressible Euler equations with linear damping
• Stochastic compressible Euler equations and inviscid limits
• Dissipative solutions and Markov selection to the complete stochastic Euler system
• From Hamiltonian Systems to Compressible Euler Equation driven by additive Hölder noise