From gas dynamics with large friction to gradient flows describing diffusion theories

Abstract

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.

Updated to Authors' Accepted Manuscript version

References in corpus (2)

• On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
• Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics

Cited by in corpus (17)

• Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
• Mean-field limits: from particle descriptions to macroscopic equations
• Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation
• High-friction limits of Euler flows for multicomponent systems
• The relaxation limit of bipolar fluid models
• Stability and asymptotic analysis for instationary gas transport via relative energy estimates
• $W$-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds
• Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems
• The role of Riesz potentials in the weak-strong uniqueness for Euler-Poisson systems
• A mode of convergence arising in diffusive relaxation
• A positivity-preserving and energy stable scheme for a quantum diffusion equation
• Parabolic-elliptic Keller-Segel's system
• Relaxation to fractional porous medium equation from Euler--Riesz system
• The time-relaxation limit for weak solutions to the quantum hydrodynamics system
• Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions
• High-friction limit for bipolar Euler-Riesz systems
• Relative Entropy Method for the relaxation limit of Hydrodynamic models