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

  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},
  • 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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