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I am interested in, broadly speaking, the analysis of nonlinear partial
differential equations. More specifically, I study (1) the Cauchy problem of nonlinear water waves,
(2) the stability/instability issue of steady solutions to the Euler equations with free boundary,
(3) solitary-wave solutions to model equations in oceanography and geophysics. |
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| initial value problem for surface water-waves | in collaboration with Hans Christianson and Gigliola Staffilani, Local smoothing effects for the water-wave problem with surface tension, 91 pages arXiv |
| research announcement of Local smoothing effects for the water-wave problem with surface tension, C. R. Math. Acad. Sci. Paris, 347, 159--162 (2009) pdf |
| nonlinear dispersive equations | in collaboration with Robin Ming Chen and Yue Liu, Solitary waves of the rotation-modified Kadomtsev-Petviashvili equation, Nonlinearity, 21, 2949--2979 (2008) pdf |
| stability of solutions to the Euler equations with free boundary | in collaboration with Zhiwu Lin, Unstable surface waves in running water, Comm. Math. Phys., 282, 733--796 (2008) pdf arXiv |
| 2D traveling water waves with vorticity |
| Symmetry of solitary water waves with vorticity Math. Res. Lett. 15, 491--510 (2008) pdf |
| Symmetry of steady periodic water waves with vorticity, Philos. Trans. R. Soc. Lond. Ser. A, 365, theme issue 'Water waves', 2203--2214 (2007) pdf |
| Exact solitary water waves with vorticity, Arch. Rat. Mech. Anal. 188, 213--244 (2008) pdf |
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Global bifurcation of deep-water waves with vorticity,
SIAM J. Math. Anal.,
37, 1482--1521 (2006)
pdf |
| I received my PhD from the Department of Mathematics at Brown University in May 2006. My advisor is Walter Strauss. |