Vera Mikyoung Hur

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The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitarywaves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a(More)
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the(More)
We study the dispersive character for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of surface tension. The main result state that, on average in time, the solution of the water-wave problem gains locally 1/4 derivative of smoothness in the spatial variable, compared to the initial state. The regularizing(More)
We study the stability and instability of periodic traveling waves for Korteweg-de Vries type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations. We then discuss when the associated linearized(More)
The rotation-modified Kadomtsev-Petviashvili equation describes small-amplitude, long internal waves propagating in one primary direction in a rotating frame of reference. The main investigation is the the existence and properties of its solitary waves. The existence and non-existence results for the solitary waves are obtained, and their regularity and(More)
We discuss certain a priori geometric properties of two-dimensional steady gravity water waves with vorticity. The main result states that for an arbitrary distribution of vorticity, any periodic wave of finite depth with a single trough (a minimum over one period) is symmetric about a single crest (a maximum over one period) and the wave profile decreases(More)
We determine the stability and instability of a sufficiently small and periodic travelling wave to long-wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium-amplitude waves. In the absence of the effects of(More)