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Global weak solutions to the Euler-Vlasov equations with finite energy. (English) Zbl 1496.35290

Summary: This paper concentrates on the global existence of weak solutions in \(L^p\) with finite energy to a type of one-dimensional compressible Euler-Vlasov equations, which models the interaction between the isentropic gas and dispersed particles. Approximate solutions are constructed by adding artificial viscosity. Then the uniform \(L^p\) estimates of the approximate solutions with respect to the artificial viscosity are established through some subtle analysis on level sets of density and relative velocity. The convergence of approximate solutions to the desired weak solutions is guaranteed by the \(L^p\) compensated compactness framework.

MSC:

35Q31 Euler equations
35Q35 PDEs in connection with fluid mechanics
35Q83 Vlasov equations
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
54D30 Compactness
76G25 General aerodynamics and subsonic flows
76N15 Gas dynamics (general theory)
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