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Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence
Upper semi-continuity of stationary statistical properties of dissipative systems
1. | Department of Mathematics, Florida State University, Tallahassee, FL32306 |
[1] |
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 |
[2] |
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 |
[3] |
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 |
[4] |
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 |
[5] |
Jungho Park. Dynamic bifurcation theory of Rayleigh-Bénard convection with infinite Prandtl number. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 591-604. doi: 10.3934/dcdsb.2006.6.591 |
[6] |
Jhean E. Pérez-López, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa. On the Rayleigh-Bénard-Marangoni problem: Theoretical and numerical analysis. Journal of Computational Dynamics, 2020, 7 (1) : 159-181. doi: 10.3934/jcd.2020006 |
[7] |
Björn Birnir, Nils Svanstedt. Existence theory and strong attractors for the Rayleigh-Bénard problem with a large aspect ratio. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 53-74. doi: 10.3934/dcds.2004.10.53 |
[8] |
Pengyu Chen, Xuping Zhang. Upper semi-continuity of attractors for non-autonomous fractional stochastic parabolic equations with delay. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4325-4357. doi: 10.3934/dcdsb.2020290 |
[9] |
Xiaohui Zhang, Xuping Zhang. Upper semi-continuity of non-autonomous fractional stochastic $ p $-Laplacian equation driven by additive noise on $ \mathbb{R}^n $. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022081 |
[10] |
Xiaoming Wang. Numerical algorithms for stationary statistical properties of dissipative dynamical systems. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4599-4618. doi: 10.3934/dcds.2016.36.4599 |
[11] |
José Antonio Carrillo, Marco Di Francesco, Antonio Esposito, Simone Fagioli, Markus Schmidtchen. Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 1191-1231. doi: 10.3934/dcds.2020075 |
[12] |
P.E. Kloeden, Pedro Marín-Rubio, José Real. Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations. Communications on Pure and Applied Analysis, 2009, 8 (3) : 785-802. doi: 10.3934/cpaa.2009.8.785 |
[13] |
Isabel Mercader, Oriol Batiste, Arantxa Alonso, Edgar Knobloch. Dissipative solitons in binary fluid convection. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1213-1225. doi: 10.3934/dcdss.2011.4.1213 |
[14] |
Yumi Yahagi. Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1497-1510. doi: 10.3934/dcdsb.2021099 |
[15] |
Marco Cabral, Ricardo Rosa, Roger Temam. Existence and dimension of the attractor for the Bénard problem on channel-like domains. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 89-116. doi: 10.3934/dcds.2004.10.89 |
[16] |
O. V. Kapustyan, V. S. Melnik, José Valero. A weak attractor and properties of solutions for the three-dimensional Bénard problem. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 449-481. doi: 10.3934/dcds.2007.18.449 |
[17] |
Jann-Long Chern, Zhi-You Chen, Yong-Li Tang. Structure of solutions to a singular Liouville system arising from modeling dissipative stationary plasmas. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2299-2318. doi: 10.3934/dcds.2013.33.2299 |
[18] |
Tomasz Szarek, Mariusz Urbański, Anna Zdunik. Continuity of Hausdorff measure for conformal dynamical systems. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4647-4692. doi: 10.3934/dcds.2013.33.4647 |
[19] |
Yuntao Zang. An upper bound of the measure-theoretical entropy. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022052 |
[20] |
Lucas Backes, Aaron Brown, Clark Butler. Continuity of Lyapunov exponents for cocycles with invariant holonomies. Journal of Modern Dynamics, 2018, 12: 223-260. doi: 10.3934/jmd.2018009 |
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