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Dynamic bifurcation theory of Rayleigh-Bénard convection with infinite Prandtl number
1. | Department of Mathematics & Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, United States |
[1] |
Tian Ma, Shouhong Wang. Attractor bifurcation theory and its applications to Rayleigh-Bénard convection. Communications on Pure and Applied Analysis, 2003, 2 (4) : 591-599. doi: 10.3934/cpaa.2003.2.591 |
[2] |
Toshiyuki Ogawa. Bifurcation analysis to Rayleigh-Bénard convection in finite box with up-down symmetry. Communications on Pure and Applied Analysis, 2006, 5 (2) : 383-393. doi: 10.3934/cpaa.2006.5.383 |
[3] |
Cheng-Jie Liu, Ya-Guang Wang, Tong Yang. Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2011-2029. doi: 10.3934/dcdss.2016082 |
[4] |
Leif Arkeryd, Raffaele Esposito, Rossana Marra, Anne Nouri. Exponential stability of the solutions to the Boltzmann equation for the Benard problem. Kinetic and Related Models, 2012, 5 (4) : 673-695. doi: 10.3934/krm.2012.5.673 |
[5] |
Shigeru Takata, Masanari Hattori, Takumu Miyauchi. On the entropic property of the Ellipsoidal Statistical model with the prandtl number below 2/3. Kinetic and Related Models, 2020, 13 (6) : 1163-1174. doi: 10.3934/krm.2020041 |
[6] |
Yukio Kan-On. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 147-162. doi: 10.3934/dcds.2002.8.147 |
[7] |
B. A. Wagner, Andrea L. Bertozzi, L. E. Howle. Positive feedback control of Rayleigh-Bénard convection. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 619-642. doi: 10.3934/dcdsb.2003.3.619 |
[8] |
Iryna Pankratova, Andrey Piatnitski. Homogenization of convection-diffusion equation in infinite cylinder. Networks and Heterogeneous Media, 2011, 6 (1) : 111-126. doi: 10.3934/nhm.2011.6.111 |
[9] |
Rana D. Parshad. Asymptotic behaviour of the Darcy-Boussinesq system at large Darcy-Prandtl number. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1441-1469. doi: 10.3934/dcds.2010.26.1441 |
[10] |
Shigeru Takata, Masanari Hattori, Takumu Miyauchi. Erratum to: On the entropic property of the ellipsoidal statistical model with the Prandtl number below 2/3. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022013 |
[11] |
Yukio Kan-On. Bifurcation structures of positive stationary solutions for a Lotka-Volterra competition model with diffusion II: Global structure. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 135-148. doi: 10.3934/dcds.2006.14.135 |
[12] |
Hideaki Takaichi, Izumi Takagi, Shoji Yotsutani. Global bifurcation structure on a shadow system with a source term - Representation of all solutions-. Conference Publications, 2011, 2011 (Special) : 1344-1350. doi: 10.3934/proc.2011.2011.1344 |
[13] |
Qiaolin He. Numerical simulation and self-similar analysis of singular solutions of Prandtl equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 101-116. doi: 10.3934/dcdsb.2010.13.101 |
[14] |
Tingyuan Deng. Three-dimensional sphere $S^3$-attractors in Rayleigh-Bénard convection. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 577-591. doi: 10.3934/dcdsb.2010.13.577 |
[15] |
Chun-Hsiung Hsia, Tian Ma, Shouhong Wang. Bifurcation and stability of two-dimensional double-diffusive convection. Communications on Pure and Applied Analysis, 2008, 7 (1) : 23-48. doi: 10.3934/cpaa.2008.7.23 |
[16] |
Joachim Naumann, Jörg Wolf. On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1371-1390. doi: 10.3934/dcdss.2013.6.1371 |
[17] |
Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 1007-1015. doi: 10.3934/dcdss.2020059 |
[18] |
Rachel Kuske, Peter Borowski. Survival of subthreshold oscillations: The interplay of noise, bifurcation structure, and return mechanism. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 873-895. doi: 10.3934/dcdss.2009.2.873 |
[19] |
Kousuke Kuto, Tohru Tsujikawa. Bifurcation structure of steady-states for bistable equations with nonlocal constraint. Conference Publications, 2013, 2013 (special) : 467-476. doi: 10.3934/proc.2013.2013.467 |
[20] |
Pengmiao Hao, Xuechen Wang, Junjie Wei. Global Hopf bifurcation of a population model with stage structure and strong Allee effect. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 973-993. doi: 10.3934/dcdss.2017051 |
2020 Impact Factor: 1.327
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