## Global discontinuous solution for $$1D$$ isentropic gas dynamics system.(English)Zbl 07441034

Summary: In this work, we study the global existence of one-dimensional isentropic gas dynamics system. We prove a global-in-time existence result of this system in the framework of discontinuous non-decreasing solutions considering bounded initial data. We remark that this result allows us to give a global meaning to the gas dynamics system in distributional sense, considering discontinuous solutions with vacuum.

### MSC:

 35Q31 Euler equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35D40 Viscosity solutions to PDEs 35F20 Nonlinear first-order PDEs 35L40 First-order hyperbolic systems 35Q31 Euler equations 74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
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