Short Time Regularity of Navier-Stokes Flows with Locally L3Initial Data and Applications

Kyungkeun Kang; Hideyuki Miura; Tai Peng Tsai

doi:10.1093/imrn/rnz327

Short Time Regularity of Navier-Stokes Flows with Locally L³Initial Data and Applications

Kyungkeun Kang, Hideyuki Miura, Tai Peng Tsai

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in L3. The result is applied to the regularity problems of solutions with uniformly small local L3 norms and of forward discretely self-similar solutions.

Original language	English
Pages (from-to)	8763-8805
Number of pages	43
Journal	International Mathematics Research Notices
Volume	2021
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnz327
Publication status	Published - 2021 Jun 1

Bibliographical note

Funding Information:
This research was supported by National Research Foundation [2017R1A2B4006484 to K.K.]; the Yonsei University Challenge of 2017 [to K.K.]; Japan Society for the Promotion of Science [grant 17K05312 to H.M.]; and Natural Sciences and Engineering Research Council of Canada [grant 261356-13 to T.-P.T.].

Publisher Copyright:
© The Author(s) 2020. Published by Oxford University Press. All rights reserved.

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1093/imrn/rnz327

Cite this

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abstract = "We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in L3. The result is applied to the regularity problems of solutions with uniformly small local L3 norms and of forward discretely self-similar solutions.",

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AU - Tsai, Tai Peng

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N2 - We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in L3. The result is applied to the regularity problems of solutions with uniformly small local L3 norms and of forward discretely self-similar solutions.

AB - We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in L3. The result is applied to the regularity problems of solutions with uniformly small local L3 norms and of forward discretely self-similar solutions.

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