Global Attractor Of 3D MHD Model In Porous Media

The magnetohydrodynamics equations form the system that governs the interaction of conducting fluids and electromagnetic forces,which aise in different disciplines and applications.Theoretically,the 3D MHD model consists of coupling the Navier-stokes equations and Maxwell's equations to control the conducting fluid and electromagnetic forces.Dynamical systems can be used to describe the asymptotic behavior of equations,especially the existence of global attractors,which is paid much attention.In this paper,the author mainly considers the global attractor problem of 3D MHD model in porous media.In order to complete the content and structure of this paper,this paper includes four chapters:The first chapter is the introduction,which mainly describes the research status of the global attractor problem of 3D MHD model,and the relevant work to be done by the author under the existing research results.The second chapter is the preliminary knowledge,which focuses on the introduction of relevant concepts,common formulas,common equation forms and important theorems,paving the way for the study of the global attractors and their properties of the 3D MHD model in porous media.The third chapter is the main conclusion.To put in detail,the author verifies that the corresponding semigroup has attractive sets by using the method of energy estimation.Furthermore,the author discusses the existence of the global attractor of the equation through the equivalent condition that the corresponding semigroup of the equation has a global attractor,and obtains clearly the continuous dependence of the solution on the initial data.And finally,the author shows that the fractal dimension of the global attractor is finite.The fourth chapter is the summary and prospect,which summarizes the main results and gives the work and the development direction needed to be done in the future.