Bifurcation and structure of solutions for fluid dynamical systems

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We are concerned mainly with fluid dynamical systems describing motions for compressible heat convection, viscous incompressible flow down an inclined plane or down a vertical plane under the gravity. After constructing resolvent operators and estimating their norms we proved existence of solutions to full nonlinear problems and studied bifurcation structure and stability of solutions. To show existence proof and asymptotic property of bifurcating solutions, it is the key point that those resolvent operator generate an analytic semigroup in a suitable function space. We proved the existence of stationary solution to the compressible heat convection and obtained the bifurcating branch from the heat conducting state.