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arXiv · 2001.01652

Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior

Paolo Antonelli·Lars Eric Hientzsch·Stefano Spirito
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Abstract

We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The vacuum regions are included in the weak formulation of the equations. Our method consists in an invading domains approach. More precisely, by using a suitable truncation argument we construct a sequence of approximate solutions. The energy and the BD entropy bounds allow for the passage to the limit in the truncated formulation leading to a finite energy weak solution. Moreover, the result is also valid in the case of compressible Navier-Stokes equations with degenerate viscosity.

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Paolo Antonelli, Lars Eric Hientzsch, Stefano Spirito. 2020-01-06. Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior. https://doi.org/10.1016/j.jde.2021.04.025

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