Research of applied analysis toward the global theory for nonlinear systems

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Analysis for the heat convectin problems for the system of Oberbeck-Boussinesq equations in the horizontal strip domain. The existence of bifurcation curve of roll-type solutions is proved for the ten times Rayleigh number of critical Rayleigh number by a computer assisted proof . The second bifurcation point of stationary roll-type solutions is determined by a computer assisted proof. The hexagonal-type and rectangle-type solutions of 3-dimensional problems are also proved for the existence by a computer assisted proof at least for rather small Rayleigh numbers.The cocoon bifurcation for the Michelson system is analyzed and proved for the existence bf infinitely many bifurcations of heteroclinic orbits to the saddle-node periodic orbit by a topological method and a computer assisted proof.The driven-cavity problem of 2-dimensional Navier-Stokes equation is solved for rather large Reynolds numbers compared to the existing verified result by a Newton type computer assited proof.