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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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems, 2021 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems, 2016, 36 (10) : 53095322. doi: 10.3934/dcds.2016033 
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