Short Time Regularity of Navier–Stokes Flows with Locally L3 Initial Data and Applications

Short Time Regularity of Navier–Stokes Flows with Locally L3 Initial Data and Applications

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 $L^3$. The result is applied to the regularity problems of solutions with uniformly small local $L^3$ norms and of forward discretely self...

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Veröffentlicht in:International mathematics research notices 2021-06, Vol.2021 (11), p.8763-8805
Hauptverfasser: Kang, Kyungkeun, Miura, Hideyuki, Tsai, Tai-Peng
Format: Artikel
Sprache:eng
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Zusammenfassung: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 $L^3$. The result is applied to the regularity problems of solutions with uniformly small local $L^3$ norms and of forward discretely self-similar solutions.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz327