Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts

doi:10.1007/s00208-020-01988-5

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	Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts
	Brue, Elia 1; Nguyen, Quoc-Hung2
	2021-06
发表期刊	MATHEMATISCHE ANNALEN
ISSN	0025-5831
EISSN	1432-1807
发表状态	已发表
DOI	10.1007/s00208-020-01988-5
摘要	It is known, after Jabin (J Differ Equ 260(5):4739-4757, 2016) and Alberti et al. (Ann PDE 5(1):9, 2019), that ODE flows and solutions of the transport equation associated to Sobolev vector fields do not propagate Sobolev regularity, even of fractional order. In this paper, we improve the result at Clop and Jylha (J Differ Equ 266(8):4544-4567, 2019) and show that some kind of propagation of Sobolev regularity happens as soon as the gradient of the drift is exponentially integrable. We provide sharp Sobolev estimates and new examples. As an application of our main theorem, we generalize a regularity result for the 2D Euler equation obtained by Bahouri and Chemin in Bahouri and Chemin (Arch Ration Mech Anal 127(2):159-181, 1994).
关键词	34A12 35F25 35F10
URL	查看原文
收录类别	SCI ; SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000527491900001
出版者	SPRINGER HEIDELBERG
WOS关键词	VECTOR-FIELDS ; REGULARITY ; SPACES
原始文献类型	Article ; Early Access
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/119469
专题	数学科学研究所_PI研究组(P)_Quoc Hung Nguyen组
通讯作者	Brue, Elia
作者单位	1.Scuola Normale Super Pisa, Pisa, Italy 2.ShanghaiTech Univ, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Brue, Elia,Nguyen, Quoc-Hung. Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts[J]. MATHEMATISCHE ANNALEN,2021.
APA	Brue, Elia,&Nguyen, Quoc-Hung.(2021).Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts.MATHEMATISCHE ANNALEN.
MLA	Brue, Elia,et al."Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts".MATHEMATISCHE ANNALEN (2021).