量子Navier-Stokes方程弱解的全局存在性

摘要/Abstract

摘要：

该文证明了在非单调压力情形下量子Navier-Stokes方程弱解的全局存在性. 受Antonelli-Spirito (Arch Ration Mech Anal, 2017, 255: 1161–1199)和Ducomet-Ne?asová-Vasseur (Z Angew Math Phys, 2010, 61: 479–491)工作的启发, 该文构造了含有冷压力项和阻尼项的逼近解系统, 然后由B-D熵估计和Mellet-Vasseur不等式得到了相应的紧性.

关键词: 量子Navier-Stokes方程, 全局存在性, 弱解, 非单调压力

Abstract:

In this paper, we proved the global existence of weak solutions to the quantum Navier-Stokes equations with non-monotone pressure. Motivated by the work of Antonelli-Spirito(Arch Ration Mech Anal, 2017, 255: 1161–1199) and Ducomet-Ne?asová-Vasseur (Z Angew Math Phys, 2010, 61: 479–491), we construct the suitable approximate system and obtain the corresponding compactness by B-D entropy estimate and Mellet-Vasseur inequality.

Key words: Quantum Navier-Stokes equation, Global existence, Weak solutions, Non-monotone pressure

中图分类号:

O175.2

唐童,牛聪. 量子Navier-Stokes方程弱解的全局存在性[J]. 数学物理学报, 2022, 42(2): 387-400.

Tong Tang,Cong Niu. Global Existence of Weak Solutions to the Quantum Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2022, 42(2): 387-400.

参考文献 37

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