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Rapid perturbational calculations for the Helmholtz equation in two dimensions
Nonexistence of locally selfsimilar blowup for the 3D incompressible NavierStokes equations
1.  Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA 91125, United States 
2.  LMAM&School of Mathematical Sciences, Peking University, Beijing, 100871, China 
[1] 
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 
[2] 
Zoran Grujić. Regularity of forwardintime selfsimilar solutions to the 3D NavierStokes equations. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 837843. doi: 10.3934/dcds.2006.14.837 
[3] 
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 
[4] 
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 
[5] 
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 
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Razvan Gabriel Iagar, Ana Isabel Muñoz, Ariel Sánchez. Selfsimilar blowup patterns for a reactiondiffusion equation with weighted reaction in general dimension. Communications on Pure and Applied Analysis, 2022, 21 (3) : 891925. doi: 10.3934/cpaa.2022003 
[7] 
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 
[8] 
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 
[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] 
Yi Zhou, Zhen Lei. Logarithmically improved criteria for Euler and NavierStokes equations. Communications on Pure and Applied Analysis, 2013, 12 (6) : 27152719. doi: 10.3934/cpaa.2013.12.2715 
[11] 
Michele Coti Zelati. Remarks on the approximation of the NavierStokes equations via the implicit Euler scheme. Communications on Pure and Applied Analysis, 2013, 12 (6) : 28292838. doi: 10.3934/cpaa.2013.12.2829 
[12] 
Carlo Morosi, Livio Pizzocchero. On the constants in a Kato inequality for the Euler and NavierStokes equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 557586. doi: 10.3934/cpaa.2012.11.557 
[13] 
Pavel I. Plotnikov, Jan Sokolowski. Compressible NavierStokes equations. Conference Publications, 2009, 2009 (Special) : 602611. doi: 10.3934/proc.2009.2009.602 
[14] 
Jan W. Cholewa, Tomasz Dlotko. Fractional NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2018, 23 (8) : 29672988. doi: 10.3934/dcdsb.2017149 
[15] 
Hamid Bellout, Jiří Neustupa, Patrick Penel. On a $\nu$continuous family of strong solutions to the Euler or NavierStokes equations with the NavierType boundary condition. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 13531373. doi: 10.3934/dcds.2010.27.1353 
[16] 
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 
[17] 
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 
[18] 
Jian Su, Yinnian He. The almost unconditional convergence of the Euler implicit/explicit scheme for the three dimensional nonstationary NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2017, 22 (9) : 34213438. doi: 10.3934/dcdsb.2017173 
[19] 
Jeongho Kim, Weiyuan Zou. Solvability and blowup criterion of the thermomechanical CuckerSmaleNavierStokes equations in the whole domain. Kinetic and Related Models, 2020, 13 (3) : 623651. doi: 10.3934/krm.2020021 
[20] 
Hermenegildo Borges de Oliveira. Anisotropically diffused and damped NavierStokes equations. Conference Publications, 2015, 2015 (special) : 349358. doi: 10.3934/proc.2015.0349 
2021 Impact Factor: 1.588
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