Lizhe Wan - Academia.edu (original) (raw)
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Università degli Studi di Napoli "Federico II"
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Papers by Lizhe Wan
arXiv (Cornell University), May 8, 2023
We consider the two dimensional pure gravity water waves with nonzero constant vorticity in infin... more We consider the two dimensional pure gravity water waves with nonzero constant vorticity in infinite depth, working in the holomorphic coordinates introduced in [32]. We show that close to the critical velocity corresponding to zero frequency, a solitary wave exists. We use a fixed point argument to construct the solitary wave whose profile resembles a rescaled Benjamin-Ono soliton. The solitary wave is smooth and has an asymptotic expansion in terms of powers of the Benjamin-Ono soliton.
arXiv (Cornell University), Aug 20, 2021
This article is concerned with infinite depth gravity water waves with constant vorticity in two ... more This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.
arXiv (Cornell University), Aug 6, 2022
We consider the L 2 well-posedness of third order Benjamin-Ono equation. We show that by means of... more We consider the L 2 well-posedness of third order Benjamin-Ono equation. We show that by means of a normal form and a gauge transformation, the equation can be changed into an Airy-type equation. A second goal of this work is to establish that the solutions to the nonlinear third order Benjamin-Ono equation problem exhibit a dispersive decay estimate analogue to the corresponding linear associated problem. The key ingredient is the use of a nonlinear vector field akin to the work in [8, 9].
arXiv (Cornell University), May 8, 2023
We consider the two dimensional pure gravity water waves with nonzero constant vorticity in infin... more We consider the two dimensional pure gravity water waves with nonzero constant vorticity in infinite depth, working in the holomorphic coordinates introduced in [32]. We show that close to the critical velocity corresponding to zero frequency, a solitary wave exists. We use a fixed point argument to construct the solitary wave whose profile resembles a rescaled Benjamin-Ono soliton. The solitary wave is smooth and has an asymptotic expansion in terms of powers of the Benjamin-Ono soliton.
arXiv (Cornell University), Aug 20, 2021
This article is concerned with infinite depth gravity water waves with constant vorticity in two ... more This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.
arXiv (Cornell University), Aug 6, 2022
We consider the L 2 well-posedness of third order Benjamin-Ono equation. We show that by means of... more We consider the L 2 well-posedness of third order Benjamin-Ono equation. We show that by means of a normal form and a gauge transformation, the equation can be changed into an Airy-type equation. A second goal of this work is to establish that the solutions to the nonlinear third order Benjamin-Ono equation problem exhibit a dispersive decay estimate analogue to the corresponding linear associated problem. The key ingredient is the use of a nonlinear vector field akin to the work in [8, 9].