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Low Mach number limit for the quantum hydrodynamics system. (English) Zbl 1344.35093

Summary: In this paper, we deal with the low Mach number limit for the system of quantum hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong convergence of the solutions toward regular solutions of the incompressible Euler system. In particular, we will perform a detailed analysis of the time oscillations and of the relative entropy functional related to the system.

MSC:

35Q35 PDEs in connection with fluid mechanics
35L65 Hyperbolic conservation laws
35L40 First-order hyperbolic systems
76R50 Diffusion
76D05 Navier-Stokes equations for incompressible viscous fluids
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76Q05 Hydro- and aero-acoustics
35B65 Smoothness and regularity of solutions to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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References:

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