TY - JOUR

T1 - On weak solutions of steady Navier-Stokes equations for monatomic gas

AU - Březina, J.

AU - Novotný, A.

N1 - Funding Information:
∗ The work has been supported by Jindˇrich Neˇcas Center for Mathematical project LC06052 financed by MSˇMT CˇR.
Publisher Copyright:
© 2008, Charles University, Faculty of Mathematics and Physics.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:77953197459

VL - 49

SP - 611

EP - 632

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

SN - 0010-2628

IS - 4

ER -