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.