Rigidity results in generalized isothermal fluids
arXiv:1803.07837 · doi:10.5802/ahl.2
Abstract
We investigate the long-time behavior of solutions to the isothermal Euler, Korteweg or quantum Navier Stokes equations, as well as generalizations of these equations where the convex pressure law is asymptotically linear near vacuum. By writing the system with a suitable time-dependent scaling we prove that the densities of global solutions display universal dispersion rate and asymptotic profile. This result applies to weak solutions defined in an appropriate way. In the exactly isothermal case, we establish the compactness of bounded sets of such weak solutions, by introducing modified entropies adapted to the new unknown functions.
arXiv comment34 pages
References in corpus (8)
- 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
- Universal dynamics for the defocusing logarithmic Schrodinger equation
- Madelung, Gross-Pitaevskii and Korteweg
- Global well-posedness of the Euler-Korteweg system for small irrotational data
- Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}
- About the barotropic compressible quantum Navier-Stokes equations