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On scaling invariance and type-Ⅰ singularities for the compressible Navier-Stokes equations

On scaling invariance and type-Ⅰ singularities for the compressible Navier-Stokes equations

作     者:Zhen Lei Zhouping Xin 

作者机构:School of Mathematical SciencesLMNS and Shanghai Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghai 200433China The Institute of Mathematical Sciences and Department of MathematicsThe Chinese University of Hong KongHong KongChina 

出 版 物:《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期:2019年第62卷第11期

页      面:2271-2286页

核心收录:

学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基  金:supported by National Natural Science Foundation of China (Grant No. 11725102) National Support Program for Young Top-Notch Talents SGST 09DZ2272900 from Shanghai Key Laboratory for Contemporary Applied Mathematics supported by Zheng Ge Ru Foundation, Hong Kong RGC Earmarked Research Grants (Grant Nos. CUHK-14305315, CUHK-14300917 and CUHK-14302917) NSFC/RGC Joint Research Scheme Grant (Grant No. N-CUHK 443-14) a Focus Area Grant from the Chinese University of Hong Kong 

主  题:type-Ⅰ singularity compressible Navier-Stokes equations scaling invariance blowup rate 

摘      要:We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here κ 0 does not depend on the initial *** is achieved by proving the regularity of solutions under■ This new scaling invariance also motivates us to construct an explicit type-Ⅱ blowup solution for γ 1.

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