Attractor And Statistical Solution For Two Kinds Of Equations In Hydromechanics

This masters thesis mainly studies the strong trajectory statistical solutions of two-dimensional dissipative Euler equations and the statis-tical solutions of three-dimensional MHD-? equations.The thesis first uses the strong trajectory attractor of the two-dimensional dissipative Euler equations to construct its strong trajectory statistical solutions of the equations and proves that the strong trajectory statistical solutions are invariant and satisfy the Liouville-type theorem.Then the thesis proves that the process generated by the solution operator of the three-dimensional MHD-? equations possesses a pullback attractor,there ex-ists a family of invariant Borel probability measures on the pullback attractor.Moreover,this family of measures satisfies the Liouville-type theorem and is a statistical solution of the MHD-? equation.