Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics

@article{Giesselmann2015RelativeEF,
  title={Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics},
  author={J. Giesselmann and C. Lattanzio and A. Tzavaras},
  journal={Archive for Rational Mechanics and Analysis},
  year={2015},
  volume={223},
  pages={1427-1484}
}
  • J. Giesselmann, C. Lattanzio, A. Tzavaras
  • Published 2015
  • Mathematics, Physics
  • Archive for Rational Mechanics and Analysis
  • AbstractWe consider a Euler system with dynamics generated by a potential energy functional. We propose a form for the relative energy that exploits the variational structure and we derive a relative energy identity. When applied to specific energies, this yields relative energy identities for the Euler–Korteweg, the Euler–Poisson, the Quantum Hydrodynamics system, and low order approximations of the Euler–Korteweg system. For the Euler–Korteweg system we prove a stability theorem between a… CONTINUE READING
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    References

    SHOWING 1-10 OF 43 REFERENCES
    Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems
    • 45
    • PDF
    On the well-posedness for the Euler-Korteweg model in several space dimensions
    • 82
    • Highly Influential
    • PDF
    On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
    • 96
    • PDF
    Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension
    • 19
    • PDF
    Structure of Korteweg models and stability of diffuse interfaces
    • 54
    • PDF