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In this article, we consider the global behavior of weak solutions of the Navier-Stokes equations of a compressible fluid in a bounded domain driven by bounded forces for the adiabatic constant γ = 5 / 3 . Under the condition of a small mass depending on the given forces, we prove the existence of bounded absorbing sets of weak solutions, and thus we further get global bounded trajectories...
We are concerned with the Dirichlet problem of the three-dimensional steady viscous compressible magnetohydrodynamic (MHD) equations. It is proved that for any specific heat ratio γ > 1 , the Dirichlet problem of the steady compressible MHD equations on a bounded domain Ω ⊂ R 3 admits a renormalized weak solution. Our method relies upon...
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