Global wellposedness of the 3-D full water wave problem

By Sijue Wu. 2011

243 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8cdb4259650839783e4618a68ddebb0ddca74e11

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Global solutions for the gravity water waves system in 2d (2013, methodology): “[Wu11] Wu, S. Global wellposedness of the 3-”
Finite time singularities for the free boundary incompressible Euler equations (2011, background): “[19], [20] and Wu [33] proved existence for all time in the case of small initial data.”
Nonlinear fractional Schrödinger equations in one dimension (2012, methodology): “In [28], as well as in [29] and [30], a nonlinear version of a normal form transformation is used in order to recast the quadratic equations into cubic ones.”
Global solutions and asymptotic behavior for two dimensional gravity water waves (2013, methodology): “Then Germain–Masmoudi–Shatah [35] and Wu [66] have shown that the Cauchy problem for three-dimensional waves is globally in time well-posed for ε small enough (with linear scattering in Germain-Masmoudi-Shatah and no assumption about the decay to 0 at spatial infinity of |Dx| 1 2 ψ in Wu).”
Finite time singularity for the modified SQG patch equation (2016, result): “We refer to [5], [4], [54], [55] for other recent advances in some of the interface problems of fluid dynamics.”
Two dimensional water waves in holomorphic coordinates II: global solutions (2014, unknown): “Without being exhaustive, we list some of the more recent references [2, 1, 5, 6, 7, 12, 4, 13, 15, 16, 18, 20, 22].”
Time quasi-periodic gravity water waves in finite depth (2017, unknown): “d = 2) it has been proved independently by GermainMasmoudi-Shatah [31] and Wu [60].”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, background): “In this irrotational case, where dispersive effects are predominant, an almost global existence result was achieved in [56] in the two-dimensional case and global existence results in three dimensions were proved recently in [19,20,57].”