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- W3100158983 abstract "We consider the 2D inviscid incompressible irrotational infinite depth water wave problem neglecting surface tension. Given wave packet initial data of the form $${epsilon B(epsilon alpha)e^{ik alpha}}$$ for k > 0, we show that the modulation of the solution is a profile traveling at group velocity and governed by a focusing cubic nonlinear Schrödinger equation, with rigorous error estimates in Sobolev spaces. As a consequence, we establish existence of solutions of the water wave problem in Sobolev spaces for times of order $${O(epsilon^{-2})}$$ provided the initial data differs from the wave packet by at most $${O(epsilon^{3/2})}$$ in Sobolev spaces. These results are obtained by directly applying modulational analysis to the evolution equation with no quadratic nonlinearity constructed in Wu (Invent Math 117(1):45–135, 2009) and by the energy method." @default.
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- W3100158983 date "2012-01-21" @default.
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- W3100158983 title "A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem" @default.
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- W3100158983 doi "https://doi.org/10.1007/s00220-012-1422-2" @default.
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