On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids
arXiv:1808.03495 · doi:10.1016/j.na.2019.03.020
Abstract
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. In contrast with previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The compactness is obtained by introducing suitable truncations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy.
arXiv commentAuthor's Accepted Version
References in corpus (13)
- Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
- Existence of Global Weak Solutions for 3D Degenerate Compressible Navier-Stokes Equations
- On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
- The Quantum Hydrodynamics system in two space dimensions
- Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
- Well/ill posedness for the Euler-Korteweg-Poisson system and related problems
- Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
- Global Existence of Finite Energy Weak Solutions of Quantum Navier-Stokes Equations
- Global well-posedness of the Euler-Korteweg system for small irrotational data
- Quasineutral limit, dispersion and oscillations for Korteweg type fluids
- On the low Mach number limit for Quantum Navier-Stokes equations
- Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations
- On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models
Cited by in corpus (5)
- Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation
- On the low Mach number limit for Quantum Navier-Stokes equations
- Global Existence of Entropy-Weak Solutions to the Compressible Navier-Stokes Equations with Non-Linear Density Dependent Viscosities
- Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior
- An intrinsically hydrodynamic approach to multidimensional QHD systems