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Regularity of forwardintime selfsimilar solutions to the 3D NavierStokes equations
1.  Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States 
[1] 
Francis Hounkpe, Gregory Seregin. An approximation of forward selfsimilar solutions to the 3D NavierStokes system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 48234846. doi: 10.3934/dcds.2021059 
[2] 
Thomas Y. Hou, Ruo Li. Nonexistence of locally selfsimilar blowup for the 3D incompressible NavierStokes equations. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 637642. doi: 10.3934/dcds.2007.18.637 
[3] 
Dongho Chae, Kyungkeun Kang, Jihoon Lee. Notes on the asymptotically selfsimilar singularities in the Euler and the NavierStokes equations. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 11811193. doi: 10.3934/dcds.2009.25.1181 
[4] 
Weronika Biedrzycka, Marta TyranKamińska. Selfsimilar solutions of fragmentation equations revisited. Discrete and Continuous Dynamical Systems  B, 2018, 23 (1) : 1327. doi: 10.3934/dcdsb.2018002 
[5] 
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 
[6] 
Qiaolin He. Numerical simulation and selfsimilar analysis of singular solutions of Prandtl equations. Discrete and Continuous Dynamical Systems  B, 2010, 13 (1) : 101116. doi: 10.3934/dcdsb.2010.13.101 
[7] 
F. Berezovskaya, G. Karev. Bifurcations of selfsimilar solutions of the FokkerPlank equations. Conference Publications, 2005, 2005 (Special) : 9199. doi: 10.3934/proc.2005.2005.91 
[8] 
Alberto Bressan, Wen Shen. A posteriori error estimates for selfsimilar solutions to the Euler equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 113130. doi: 10.3934/dcds.2020168 
[9] 
Hyungjin Huh. Selfsimilar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations and Control Theory, 2018, 7 (1) : 5360. doi: 10.3934/eect.2018003 
[10] 
Marco Cannone, Grzegorz Karch. On selfsimilar solutions to the homogeneous Boltzmann equation. Kinetic and Related Models, 2013, 6 (4) : 801808. doi: 10.3934/krm.2013.6.801 
[11] 
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 
[12] 
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 
[13] 
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 
[14] 
Hideo Kubo, Kotaro Tsugawa. Global solutions and selfsimilar solutions of the coupled system of semilinear wave equations in three space dimensions. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 471482. doi: 10.3934/dcds.2003.9.471 
[15] 
Jochen Merker, Aleš Matas. Positivity of selfsimilar solutions of doubly nonlinear reactiondiffusion equations. Conference Publications, 2015, 2015 (special) : 817825. doi: 10.3934/proc.2015.0817 
[16] 
Kin Ming Hui. Existence of selfsimilar solutions of the inverse mean curvature flow. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 863880. doi: 10.3934/dcds.2019036 
[17] 
Bendong Lou. Selfsimilar solutions in a sector for a quasilinear parabolic equation. Networks and Heterogeneous Media, 2012, 7 (4) : 857879. doi: 10.3934/nhm.2012.7.857 
[18] 
Shota Sato, Eiji Yanagida. Singular backward selfsimilar solutions of a semilinear parabolic equation. Discrete and Continuous Dynamical Systems  S, 2011, 4 (4) : 897906. doi: 10.3934/dcdss.2011.4.897 
[19] 
Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to selfsimilar solutions for a semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 703716. doi: 10.3934/dcds.2008.21.703 
[20] 
Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled NavierStokes equations and nonlinear Fokker Planck equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 11851196. doi: 10.3934/dcds.2010.26.1185 
2021 Impact Factor: 1.588
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