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Mechanism of the formation of singularities for diagonal systems with linearly degenerate characteristic fields
Turbulence models, $p$fluid flows, and $W^{2, L}$ regularity of solutions
1.  Department of Applied Mathematics "U.Dini", Via F. Buonarroti 1/C, 56127Pisa, Italy 
[1] 
Xulong Qin, ZhengAn Yao. Global solutions of the free boundary problem for the compressible NavierStokes equations with densitydependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 10411052. doi: 10.3934/cpaa.2010.9.1041 
[2] 
Hantaek Bae. Solvability of the free boundary value problem of the NavierStokes equations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 769801. doi: 10.3934/dcds.2011.29.769 
[3] 
Hongjie Dong, Kunrui Wang. Interior and boundary regularity for the NavierStokes equations in the critical Lebesgue spaces. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 52895323. doi: 10.3934/dcds.2020228 
[4] 
Xulong Qin, ZhengAn Yao, Hongxing Zhao. One dimensional compressible NavierStokes equations with densitydependent viscosity and free boundaries. Communications on Pure and Applied Analysis, 2008, 7 (2) : 373381. doi: 10.3934/cpaa.2008.7.373 
[5] 
Yuming Qin, Lan Huang, Shuxian Deng, Zhiyong Ma, Xiaoke Su, Xinguang Yang. Interior regularity of the compressible NavierStokes equations with degenerate viscosity coefficient and vacuum. Discrete and Continuous Dynamical Systems  S, 2009, 2 (1) : 163192. doi: 10.3934/dcdss.2009.2.163 
[6] 
Vittorino Pata. On the regularity of solutions to the NavierStokes equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 747761. doi: 10.3934/cpaa.2012.11.747 
[7] 
Igor Kukavica. On regularity for the NavierStokes equations in Morrey spaces. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 13191328. doi: 10.3934/dcds.2010.26.1319 
[8] 
Igor Kukavica. On partial regularity for the NavierStokes equations. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 717728. doi: 10.3934/dcds.2008.21.717 
[9] 
Alessio Falocchi, Filippo Gazzola. Regularity for the 3D evolution NavierStokes equations under Navier boundary conditions in some Lipschitz domains. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 11851200. doi: 10.3934/dcds.2021151 
[10] 
Michal Beneš. Mixed initialboundary value problem for the threedimensional NavierStokes equations in polyhedral domains. Conference Publications, 2011, 2011 (Special) : 135144. doi: 10.3934/proc.2011.2011.135 
[11] 
Wenjun Wang, Lei Yao. Spherically symmetric NavierStokes equations with degenerate viscosity coefficients and vacuum. Communications on Pure and Applied Analysis, 2010, 9 (2) : 459481. doi: 10.3934/cpaa.2010.9.459 
[12] 
Zilai Li, Zhenhua Guo. On free boundary problem for compressible navierstokes equations with temperaturedependent heat conductivity. Discrete and Continuous Dynamical Systems  B, 2017, 22 (10) : 39033919. doi: 10.3934/dcdsb.2017201 
[13] 
Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the NavierStokes equations. Discrete and Continuous Dynamical Systems  S, 2013, 6 (5) : 12771289. doi: 10.3934/dcdss.2013.6.1277 
[14] 
Jishan Fan, Yasuhide Fukumoto, Yong Zhou. Logarithmically improved regularity criteria for the generalized NavierStokes and related equations. Kinetic and Related Models, 2013, 6 (3) : 545556. doi: 10.3934/krm.2013.6.545 
[15] 
Chongsheng Cao. Sufficient conditions for the regularity to the 3D NavierStokes equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 11411151. doi: 10.3934/dcds.2010.26.1141 
[16] 
Zijin Li, Xinghong Pan. Some Remarks on regularity criteria of Axially symmetric NavierStokes equations. Communications on Pure and Applied Analysis, 2019, 18 (3) : 13331350. doi: 10.3934/cpaa.2019064 
[17] 
Xuanji Jia, Zaihong Jiang. An anisotropic regularity criterion for the 3D NavierStokes equations. Communications on Pure and Applied Analysis, 2013, 12 (3) : 12991306. doi: 10.3934/cpaa.2013.12.1299 
[18] 
Keyan Wang. On global regularity of incompressible NavierStokes equations in $\mathbf R^3$. Communications on Pure and Applied Analysis, 2009, 8 (3) : 10671072. doi: 10.3934/cpaa.2009.8.1067 
[19] 
Hui Chen, Daoyuan Fang, Ting Zhang. Regularity of 3D axisymmetric NavierStokes equations. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 19231939. doi: 10.3934/dcds.2017081 
[20] 
Yukang Chen, Changhua Wei. Partial regularity of solutions to the fractional NavierStokes equations. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 53095322. doi: 10.3934/dcds.2016033 
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