On convergence of approximate solutions to the compressible Euler system

  title={On convergence of approximate solutions to the compressible Euler system},
  author={Eduard Feireisl and Martina Hofmanov'a},
  journal={Annals of PDE},
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence either (i) converges strongly in the energy norm, or (ii) the limit is not a weak solution of the associated Euler system. This is in sharp contrast to the incompressible case, where (oscillatory) approximate solutions may converge weakly to solutions of the… 
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