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Abstract:
This special session focuses on the dynamic properties of fluids and nonlinear waves arsing in models such as Euler and Navier-Stokes equations, water wave and the model equations (KDV, Bousinesq etc.), nonlinear Schrodinger equations for Bose-Einstein condensates. The main aspects include the global well-posedness of solutions, stability/instability and nearby local qualitative structures (e.g. invariant manifolds) of coherent states, long time behaviors of general solutions etc. The theory and the methods applied on these problems address some of the most advanced development in the field.
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