带有分数阶耗散的Boussinesq方程组关于速度的对数型正则准则
The Logarithmic Regularity Criteria for Velocity of Boussinesq Equations with Fractional Laplacian Dissipation
DOI: 10.12677/AAM.2021.109305, PDF,   
作者: 乐爱庭：浙江师范大学数学与计算机科学学院，浙江 金华
关键词: 分数阶耗散；Boussinesq方程组；正则性准则；Fractional Laplacian Dissipation； Boussinesq Equations； Regularity Criteria
摘要: 本文主要研究3维情形下带有分数阶耗散的Boussinesq方程组在乘子空间中的对数型正则性准则问题，证明了当速度满足(2.1)时，方程组(1.1)的弱解在(0,T]上是正则的。
Abstract: In this paper, we focus on the logarithmic regularity problem of 3D Boussinesq equations with fractional laplacian dissipation in the multiplicator space. We prove that if the velocity satisfies the condition (2.1), the weak solutions of equations (1.1) are regularity on (0,T].
文章引用：乐爱庭. 带有分数阶耗散的Boussinesq方程组关于速度的对数型正则准则[J]. 应用数学进展, 2021, 10(9): 2917-2922. https://doi.org/10.12677/AAM.2021.109305

参考文献

[1] Abidi, H. and Hmidi, T. (2007) On the Global Well-Posedness for Boussinesq System. Journal of Differential Equations, 233, 199-220. [Google Scholar] [CrossRef] 
[2] Danchin, R. and Paicu, M. (2008) Existence and Uniqueness Results for the Boussinesq System with Data in Lorentz Spaces. Physica D: Nonlinear Phenomena, 237, 1444-1460. [Google Scholar] [CrossRef] 
[3] Zhou, D.G. and Li, Z.L. (2017) Global Well-Posedness for the 2D Boussinesq Equation with Zero Viscosity. Journal of Mathematical Analysis and Applications, 447, 1072-1079. [Google Scholar] [CrossRef] 
[4] Xu, X.J. (2010) Global Regularity of Solutions of 2D Boussinesq Equations with Fractional Diffusion. Nonlinear Analysis: Theory, Methods & Applications, 172, 677-681. [Google Scholar] [CrossRef] 
[5] Qiu, H., Du, L. and Yao, Z.A. (2011) Blow-Up Criteria 3D Boussinesq Equationsin the Multiplier Spaces. Communications in Nonlinear Science and Numerical Simulation, 16, 1820-1824. [Google Scholar] [CrossRef] 
[6] Stefanov, A. and Wu, J.A. (2014) Global Regularity Result for the Boussinesq Equation with Critical Dissipation. Mathematics, 29, 195-205.
[7] Fang, D.Y., Qian, C.Y. and Zhang, T. (2016) Global Well-Posedness for 2D Boussinesq System with General Super-Critical Dissipation. Nonlinear Analysis: Real World Applications, 27, 326-349. [Google Scholar] [CrossRef] 
[8] Wu, J.H., Xu, X.J., Xue, L.T. and Ye, Z. (2016) Regularity Results for the 2D Boussinesq Equations with Critical and Supercritical Dissipation. Communications in Mathematical Sciences, 14, 1963-1997. [Google Scholar] [CrossRef] 
[9] Qiu, H., Du, Y. and Yao, Z.A. (2010) Serrin-Type Blow-Up Criteria for Three-Dimensional Boussinesq Equations. Applicable Analysis, 89, 1603-1613. [Google Scholar] [CrossRef] 
[10] Xu, F.Y., Zhang, Q. and Zhang, X.X. (2012) Regularity Criteria of the 3D Boussinesq Equations in the Morrey-Campanato Spaces. Acta Applicandae Mathematicae, 121, 231-240. [Google Scholar] [CrossRef] 
[11] Zhang, Z. (2016) Global Regularity Criteria for the n-Dimensional Boussinesq Equations with Fractional Dissipation. Journal of Differential Equations, 99, 1-5.

为你推荐