Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws

被引：23

作者：

Bardos, C. ^{[1
]}

Gwiazda, P. ^{[2
]}

Swierczewska-Gwiazda, A. ^{[3
]}

Titi, E. S. ^{[4
,5
,6
]}

Wiedemann, E. ^{[7
]}

机构：

[1] Lab JL Lions, BP187, F-75252 Paris 05, France

[2] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

[3] Univ Warsaw, Inst Appl Math & Mech, Banacha 2, PL-02097 Warsaw, TX, Poland

[4] Texas A&M Univ, Dept Math, 3368 TAMU, College Stn, TX 77843 USA

[5] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

[6] Weizmann Inst Sci, Dept Comp Sci & Appl Math, IL-76100 Rehovot, Israel

[7] Univ Ulm, Inst Appl Anal, Helmholtzstr 18, D-89081 Ulm, Germany

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2019年 / 475卷 / 2230期

关键词：

Onsager's conjecture; conservation laws; conservation of entropy; ENERGY-CONSERVATION; WEAK SOLUTIONS; INCOMPRESSIBLE EULER; IDEAL HYDRODYNAMICS; DISSIPATION; VISCOSITY; EQUATIONS;

D O I：

10.1098/rspa.2019.0289

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary. This extends various recent results of the authors.

引用

页数：18

共 28 条

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