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On the radial weak solutions of a conservative system modeling the isentropic flow. (English) Zbl 1052.35122

This paper deals with the existence of global weak solutions for the quasilinear hyperbolic system with a singular source term: \[ a_t+ (au)_x+ \frac {2au}{x}=0, \quad x>0,\;t\geq 0, \qquad u_t+ \tfrac 12 (a^2+u^2)_x=0 \] with the initial data \((a(x,0),u(x,0))= (a_0(x), u_0(x))\), \(x>0\).

MSC:

35L65 Hyperbolic conservation laws
35Q35 PDEs in connection with fluid mechanics
74N10 Displacive transformations in solids
35L45 Initial value problems for first-order hyperbolic systems
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