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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:290

Article

Antonelli, Paolo¹  Hientzsch, Lars Eric²  Spirito, Stefano³ 

[1] Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy

[2] Univ Grenoble Alpes, Inst Fourier, CNRS, 100 Rue Math, F-38610 Gieres, France

[3] Univ Aquila, DISIM Dipartimento Ingn & Sci Informaz & Matemat, Via Vetoio, I-67100 Laquila, Italy

关键词: Compressible fluids;    Quantum Navier-Stokes equation;    Degenerate viscosity;    Global existence;    Far-fieldbehavior;    Vacuum;   

DOI  :  10.1016/j.jde.2021.04.025

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free