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A Class of Global Non-smooth Axisymmetric Solutions to the Euler Equations of an Isentropic Perfect Gas in 2 Space Dimensions

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

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  • Paul Godin

    (Université Libre de Bruxelles, Département de Mathématiques)

Abstract

In papers by Serre [6], Grassin-Serre [3], and Grassin [2], global existence results were obtained for solutions to the Euler equations of a perfect gas, under some smoothness and growth assumptions on the initial data, provided the initial velocity is dispersive and the initial sound speed is small (in some norm). In this note we shall describe some results contained in [1]. We consider axisymmetric flows (for the isentropic Euler equations of a perfect gas) in 2 space dimensions, with non smooth initial data. More precisely, we consider the case that initial gradients may jump across a given circle (centered at 0); the tangential component of the initial velocity may also jump there. In each component of the complement of this circle, we assume that the initial data are restrictions of global rotation (round 0) invariant data which satisfy the assumptions of Grassin-Serre and Grassin. We describe results of [1] about global existence of a solution with the given initial data. The proof relies on some previous work of Li-Yu [4] and Li [5]. Our results are stated in Section 2. Some ideas of the proof are given in Section 3.

Suggested Citation

  • Paul Godin, 2003. "A Class of Global Non-smooth Axisymmetric Solutions to the Euler Equations of an Isentropic Perfect Gas in 2 Space Dimensions," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 549-555, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_51
    DOI: 10.1007/978-3-642-55711-8_51
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