On the infinite Prandtl number limit in two-dimensional magneto-convection
نویسندگان
چکیده
منابع مشابه
Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions
This paper examines the bifurcation and structure of the bifurcated solutions of the two-dimensional infinite Prandtl number convection problem. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [14]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and that it is homeomorphic to S1. By thor...
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We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.
متن کاملBifurcation of Infinite Prandtl Number Rotating Convection
We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...
متن کاملAddendum to the Paper ”two-dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions, J.
The main objective of this addendum to the mentioned article [49] by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to comment and list some related literatures, without any intention to provide a complete survey. For steady state PDE bifurcation problems, the often used c...
متن کاملStructure of bifurcated solutions of two-dimensional infinite Prandtl number convection with no-slip boundary conditions
We consider the two-dimensional infinite Prandtl number convection problem with no-slip boundary conditions. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [15]. The no-stress case has been examined in [16]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and it is homeomorphic to S. By ...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Real World Applications
سال: 2019
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2018.09.009