We prove weak–strong uniqueness results for the isentropic compressible Navier–Stokes system on the torus. In other words, we give conditions on a weak solution, such as the ones built up by Lions (Compressible Models, Oxford Science, Oxford, 1998), so that it is unique. It is of fundamental importance since uniqueness of these solutions is not known in general. We present two different methods, one using relative entropy, the other one using an improved Gronwall inequality due to the author; these two approaches yield complementary results. Known weak–strong uniqueness results are improved and classical uniqueness results for this equation follow naturally.
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Shenzhen Univ, Sch Math Sci, Shenzhen 518060, Peoples R ChinaShenzhen Univ, Sch Math Sci, Shenzhen 518060, Peoples R China
Duan, Qin
Huang, Xiangdi
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Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Chinese Acad Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R ChinaShenzhen Univ, Sch Math Sci, Shenzhen 518060, Peoples R China
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Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R ChinaXiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Tan Zhong
Zhang Yinghui
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Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Hunan Inst Sci & Technol, Dept Math, Yueyang 414006, Peoples R ChinaXiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
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Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Peoples R ChinaXiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
He, Lianhua
Tan, Zhong
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Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R ChinaXiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China