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Well-Posedness of the IBVPs for the 1D Viscous Gas Equations

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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  • Alexander Zlotnik

    (Department of Mathematics, National Research University Higher School of Economics, Faculty of Economic Sciences)

Abstract

The inhomogeneous initial-boundary value problems (IBVPs) are posed for the Navier-Stokes systems of equations describing the viscous barotropic and heat-conducting gas 1D flow in the Lagrangian mass coordinates. Weak solutions are studied without any restrictions on the magnitude of norms of data. Assumptions on the data are genuinely general, in particular, the initial data are taken from the Lebesgue spaces, the contact problems for different gases are covered, etc. Both the global in time existence of the weak solutions as well as their uniqueness and Lipschitz continuous dependence on data are proved thus ensuring the well-posedness of the IBVPs. The regularity issue is studied as well.

Suggested Citation

  • Alexander Zlotnik, 2018. "Well-Posedness of the IBVPs for the 1D Viscous Gas Equations," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 43, pages 2421-2493, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_33
    DOI: 10.1007/978-3-319-13344-7_33
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