Blowup criterion for Navier–Stokes equation in critical Besov space with spatial dimensions d ≥ 4

  • Kuijie Li

    LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Baoxiang Wang

    LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
Blowup criterion for Navier–Stokes equation in critical Besov space with spatial dimensions d ≥ 4 cover

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Abstract

This paper is concerned with the blowup criterion for mild solution to the incompressible Navier–Stokes equation in higher spatial dimensions . By establishing an regularity criterion in the spirit of [11], we show that if the mild solution u with initial data in , becomes singular at a finite time , then

The corresponding result in 3D case has been obtained in [24]. As a by-product, we also prove a regularity criterion for the Leray–Hopf solution in the critical Besov space, which generalizes the results in [17], where blowup criterion in critical Lebesgue space is addressed.

Cite this article

Kuijie Li, Baoxiang Wang, Blowup criterion for Navier–Stokes equation in critical Besov space with spatial dimensions d ≥ 4. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 6, pp. 1679–1707

DOI 10.1016/J.ANIHPC.2019.02.003