On a blow-up criterion for solution of 3D fractional Navier-Stokes-Coriolis equations in Lei-Lin-Gevrey spaces-Reference-Cited by-同舟云学术

On a blow-up criterion for solution of 3D fractional Navier-Stokes-Coriolis equations in Lei-Lin-Gevrey spaces

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Sun Xiaochun¹,Xu Gaoting¹,Wu Yulian¹

Affiliation:

1. School of Mathematics and Statistics, Northwest Normal University , Lanzhou , 730070 , China

Abstract

Abstract In this article, we researched the existence of the solution to the fractional Navier-Stokes equations with the Coriolis force under initial data, which belong to the Lei-Lin-Gevrey spaces. Moreover, we showed a blow-up criterion, i.e., when the maximal time of existence

T *

{T}^{* }

is finite, we proved that the norm of this same solution, in a specific Lei-Lin-Gevrey space, goes to infinity, as time tends to the maximal time of its existence.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0170/pdf

Reference19 articles.

1. A. Babin, A. Mahalov, and B. Nicolaenko, Global regularity of 3D rotating Navier-Stokes equations for resonant domains, Appl. Math. Lett. 13 (2000), no. 4, 51–57, DOI: https://doi.org/10.1016/S0893-9659(99)00208-6.

2. A. Babin, A. Mahalov, and B. Nicolaenko, Regularity and integrability of 3D Euler and Navier-Stokes equations for rotating fluids, Asymptot. Anal. 15 (1997), no. 2, 103–150.

3. W. H. Wang and G. Wu, Global mild solution of stochastic generalized Navier-Stokes equations with Coriolis force, Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 11, 1635–1647, DOI: https://doi.org/10.1007/s10114-018-7482-2.

4. T. Iwabuchi and R. Takada, Global solutions for the Navier-Stokes equations in the rotational framework, Math. Ann. 357 (2013), no. 2, 727–741, DOI: https://doi.org/10.1007/s00208-013-0923-4.

5. T. Iwabuchi and R. Takada, Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type, J. Funct. Anal. 267 (2014), no. 5, 1321–1337, DOI: https://doi.org/10.1016/j.jfa.2014.05.022.