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Two-phase flows: non-smooth well posedness and the compressible to incompressible limit. (English) Zbl 1254.76119

Summary: This paper presents a model for 2 inviscid, immiscible, compressible and isentropic fluids in 1 space dimension. Its well posedness is proved, globally in time, for data having small total variation. In a sample non-smooth case, the limit in which one of the fluids becomes incompressible is characterized.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35Q35 PDEs in connection with fluid mechanics
76T99 Multiphase and multicomponent flows
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