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Solvability of some partial integral equations in Hilbert space
Local existence and blowup criterion of the Lagrangian averaged Euler equations in Besov spaces
1. | The Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
2. | The Department of Mathematics, Huashi Da University, Shanghai, 200333, China |
[1] |
Daoyuan Fang, Chenyin Qian. Regularity criterion for 3D Navier-Stokes equations in Besov spaces. Communications on Pure and Applied Analysis, 2014, 13 (2) : 585-603. doi: 10.3934/cpaa.2014.13.585 |
[2] |
Franco Flandoli, Dejun Luo. Euler-Lagrangian approach to 3D stochastic Euler equations. Journal of Geometric Mechanics, 2019, 11 (2) : 153-165. doi: 10.3934/jgm.2019008 |
[3] |
Xinwei Yu, Zhichun Zhai. On the Lagrangian averaged Euler equations: local well-posedness and blow-up criterion. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1809-1823. doi: 10.3934/cpaa.2012.11.1809 |
[4] |
T. Tachim Medjo. Averaging of a 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external forces. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1281-1305. doi: 10.3934/cpaa.2011.10.1281 |
[5] |
Marcel Oliver. The Lagrangian averaged Euler equations as the short-time inviscid limit of the Navier–Stokes equations with Besov class data in $\mathbb{R}^2$. Communications on Pure and Applied Analysis, 2002, 1 (2) : 221-235. doi: 10.3934/cpaa.2002.1.221 |
[6] |
Sadek Gala. A new regularity criterion for the 3D MHD equations in $R^3$. Communications on Pure and Applied Analysis, 2012, 11 (3) : 973-980. doi: 10.3934/cpaa.2012.11.973 |
[7] |
Xuanji Jia, Zaihong Jiang. An anisotropic regularity criterion for the 3D Navier-Stokes equations. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1299-1306. doi: 10.3934/cpaa.2013.12.1299 |
[8] |
Ahmad Mohammad Alghamdi, Sadek Gala, Chenyin Qian, Maria Alessandra Ragusa. The anisotropic integrability logarithmic regularity criterion for the 3D MHD equations. Electronic Research Archive, 2020, 28 (1) : 183-193. doi: 10.3934/era.2020012 |
[9] |
Ming Lu, Yi Du, Zheng-An Yao, Zujin Zhang. A blow-up criterion for the 3D compressible MHD equations. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1167-1183. doi: 10.3934/cpaa.2012.11.1167 |
[10] |
T. Tachim Medjo. A non-autonomous 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external force and its global attractor. Communications on Pure and Applied Analysis, 2011, 10 (2) : 415-433. doi: 10.3934/cpaa.2011.10.415 |
[11] |
Alexei Ilyin, Anna Kostianko, Sergey Zelik. Trajectory attractors for 3D damped Euler equations and their approximation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 2275-2288. doi: 10.3934/dcdss.2022051 |
[12] |
Xiaoping Zhai, Yongsheng Li, Wei Yan. Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1865-1884. doi: 10.3934/cpaa.2015.14.1865 |
[13] |
Vladimir Angulo-Castillo, Lucas C. F. Ferreira. Long-time solvability in Besov spaces for the inviscid 3D-Boussinesq-Coriolis equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4553-4573. doi: 10.3934/dcdsb.2020112 |
[14] |
Jishan Fan, Fucai Li, Gen Nakamura. A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1757-1766. doi: 10.3934/dcdsb.2018079 |
[15] |
Claude Bardos, E. S. Titi. Loss of smoothness and energy conserving rough weak solutions for the $3d$ Euler equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 185-197. doi: 10.3934/dcdss.2010.3.185 |
[16] |
Thomas Y. Hou, Zuoqiang Shi. Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1449-1463. doi: 10.3934/dcds.2012.32.1449 |
[17] |
Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid. Evolution Equations and Control Theory, 2019, 8 (3) : 503-542. doi: 10.3934/eect.2019025 |
[18] |
Anthony Suen. Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1775-1798. doi: 10.3934/dcds.2020093 |
[19] |
Yong Zhou. Remarks on regularities for the 3D MHD equations. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 881-886. doi: 10.3934/dcds.2005.12.881 |
[20] |
Hyeong-Ohk Bae, Bum Ja Jin. Estimates of the wake for the 3D Oseen equations. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 1-18. doi: 10.3934/dcdsb.2008.10.1 |
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