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Global BV solutions of compressible Euler equations with spherical symmetry and damping. (English) Zbl 0916.35090
The authors examine the compressible Euler equations which describe spherically symmetric isentropic flows in a medium with friction. The equation of state has the form \(p= a^2 \rho^\gamma\), \(a,\gamma= \text{const}\), \(\gamma>0\). The main purpose is to investigate the combined effect of spherical symmetry and frictional damping on the total variation of the solution. To this end, the authors employ a fractional-step version of the Glimm finite difference scheme. For the particular case \(\gamma= 1\) this allows to construct an appropriate measure for the wave strengths in terms of Riemann invariants and to prove the uniform boundedness of the BV norm of approximate difference solutions. As a result, this estimate implies the global existence of BV solutions for the original problem.
Reviewer: O.Titow (Berlin)

35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI
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