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- W4300628181 abstract "We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in the hydrodynamic limit, from the particle-fluid equations that are frequently used to study the medical sprays, aerosols and sedimentation problems. For the proposed system, we first construct the local-in-time classical solutions in an appropriate $L^2$ Sobolev space. We also establish the emph{a priori} large-time behavior estimate by constructing a Lyapunov functional measuring the fluctuation of momentum and mass from the averaged quantities, and using this together with the bootstrapping argument, we obtain the global classical solution. The large-time behavior estimate asserts that the velocity functions of the pressureless Euler and the compressible Navier-Stokes equations are aligned exponentially fast as time tends to infinity." @default.
- W4300628181 created "2022-10-03" @default.
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- W4300628181 date "2016-04-17" @default.
- W4300628181 modified "2023-09-27" @default.
- W4300628181 title "The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations" @default.
- W4300628181 doi "https://doi.org/10.48550/arxiv.1604.04886" @default.
- W4300628181 hasPublicationYear "2016" @default.
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