Dynamical transition and bifurcation of hydromagnetic convection in a rotating fluid layer

Math Methods in App Sciences

et al. 2023

Self Cite

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case.

Section: Introductionmentioning

confidence: 99%

On dynamics of double‐diffusive magneto‐convection in a non‐Newtonian fluid layer

Fan

Math Methods in App Sciences

et al. 2023

Self Cite

“…We also recommend the review of Proctor and Weiss [24] and the references within for an overall understanding of the linear theory and some new results in the non-linear regime. Regarding phase transition dynamics of magneto-convection, Wang and Sengul [25] studied the dynamic transition of the incompressible MHD equations in a rectangular domain with a large magnetic Prandtl number, and diverse convection patterns is obtained depending on the choice of parameters; More recently, Li et al [26] established a complete stability and bifurcation analysis for a rotating electrically conducting fluid layer in the presence of an external magnetic field based on the Boussinesq approximation.…”

Section: Introductionmentioning

confidence: 99%

On Dynamics of Double-Diffusive Magnetoconvection in a Non-Newtonian Fluid Layer

Fan

et al. 2022

Preprint

Self Cite

This article concerns the dynamic transitions of a non-Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is done by deriving the principle of exchange of stability condition, which shows the system loses stability when thermal Rayleigh number exceeds a critical threshold. Second, we considered the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transitions, as well as the stable convection patterns. Our results show that when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, both continuous and jump transitions can occur for certain parameters; and if the diffusivities from big to small is the inverse of the previous case, only continuous transition induced by real eigenvalues are observed, which indicate a stationary convection.

Global Attractors for a Class of Weakly Damped Wave Equations with Gradient Type Nonlinearity

Wang

Shuai

2022

J Nonlinear Math Phys

In this paper, the main purpose is to study existence of the global attractor for the weakly damped wave equation with gradient type nonlinearity. To this end, we first verify the existence and uniqueness of global weak solution by the Galerkin method and compulsively variational method. Furthermore, we obtained the global strong solution under some mild assumptions on f. Secondly, we utilize the $$\omega$$ ω -limit compactness to show the semigroup generated by the equation has a compact, connected and invariant attractor.