Study on the change of patterns of vortices and waves in fluid flow.

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MIYAKAWA studied the flows of a viscous incompressible fluid in two and three-dimensional exterior domains and clarified explicit relationship between the space-time decay rates of flows and the symmetry of solutions of the equations of motion. He obtained almost complete results in the case of two space dimensions. FUKUMOTO studied the evolution of viscous vortices, applying the singular perturbation method to the non-local induction model, and obtained new results on the topological change of vortex filaments and rings. HISHIDA studied the viscous flow around a rotating body and proved for the first time the existence of stationary and nonstationary flows by finding a new class of singular integral operators. He also gave a new existence result for flows in domains with apertures. IGUCHI applied the method for treating free-surface problem to the equation of one-dimensional gas dymanics and gave a completely new approach to this problem which has wide applications to equations of similar types. He also classified the shape of free surfaces associated with shallow water flow with periodic bottom, applying the bifurcation theory.