We use L∞ estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant γ > 1 3 (1 + √13) ≈ 1.53 for the flows powered by volume non-potential forces and with γ > 1 8 (3 + √41) ≈ 1.175 for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge, it is the first result that treats in three dimensions existence of weak solutions in the physically relevant case γ ≤ 5 3 with arbitrary large external data. The solutions are constructed in a rectangular domain with periodic boundary conditions.
|Number of pages||22|
|Journal||Commentationes Mathematicae Universitatis Carolinae|
|Publication status||Published - 2008|
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