Convergence of a low order non-local Navier–Stokes–Korteweg system: The order-parameter model

DOI10.3233/ASY-161390zbMath1360.35168arXiv1302.2617OpenAlexW2962760091MaRDI QIDQ2963756

Frédéric Charve

Publication date: 21 February 2017

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2617

zbMATH Keywords

Besov spacescompressible Navier-Stokes systemLagrangian change of variableslocal and non-local capillarity

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Variational methods applied to problems in fluid mechanics (76M30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Liquid-gas two-phase flows, bubbly flows (76T10) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (5)

Asymptotics and lower bound for the lifespan of solutions to the primitive equations ⋮ Lagrangian Methods for a General Inhomogeneous Incompressible Navier--Stokes--Korteweg System with Variable Capillarity and Viscosity Coefficients ⋮ Local in time results for local and non-local capillary Navier-Stokes systems with large data ⋮ Existence of global strong solution for Korteweg system with large infinite energy initial data ⋮ A priori estimates for the 3D quasi-geostrophic system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of global strong solutions in critical spaces for barotropic viscous fluids
• A global existence result for the compressible Navier--Stokes equations in the critical \(L ^{p }\) framework
• On the global well-posedness of the Euler-Boussinesq system with fractional dissipation
• Existence of strong solutions for nonisothermal Korteweg system
• On the thermomechanics of interstitial working
• Hydrodynamics in Besov spaces
• Global existence in critical spaces for compressible Navier-Stokes equations
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Phase transitions and hysteresis in nonlocal and order-parameter models
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
• On a Lagrangian method for the convergence from a non-local to a local Korteweg capillary fluid model
• Hölder regularity of the viscous vortex patches. (Régularité höldérienne des poches de tourbillon visqueuses).
• Existence of a Global Strong Solution and Vanishing Capillarity-Viscosity Limit in One Dimension for the Korteweg System
• Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows
• Fourier Analysis and Nonlinear Partial Differential Equations
• UNIFORM ESTIMATES FOR TRANSPORT-DIFFUSION EQUATIONS
• CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY
• On the Global Well-Posedness of the Critical Quasi-Geostrophic Equation
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Convergence of capillary fluid models: from the non-local to the local Korteweg model
• On the signs of the v-derivatives of the modified Bessel functions Iv(x) and Kv(x)
• On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions

This page was built for publication: Convergence of a low order non-local Navier–Stokes–Korteweg system: The order-parameter model