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Browsing by Author "Zhu, Benben"

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    Almost well-posedness of the full water wave equation on the finite stripe domain
    Zhu, Benben (Virginia Tech, 2023-08-18)
    The dissertation gives a rigorous study of surface waves on water of finite depth subjected to gravitational force. As for `water', it is an inviscid and incompressible fluid of constant density and the flow is irrotational. The fluid is bounded above by a free surface separating the fluid from the air above (assumed to be a vacuum) and below by a rigid flat bottom. Then, the governing equations for the motion of the fluid flow are called Euler equations. If the initial fluid flow is prescribed at time zero, i.e., mathematically the initial condition for the Euler equations is given, the long-time existence of a unique solution for the Euler equations is still an open problem, even if the initial condition is small (or initial flow is almost motionless). The dissertation tries to make some progress for proving the long-time existence and show that the time interval of the existence is exponentially long, called almost global well-posedness, if the initial condition is small and satisfies some conditions. The main ideas for the study are from the corresponding almost global well-posedness result for surface waves on water of infinite depth.