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pro vyhledávání: '"Forlano, Justin"'
Autor:
Forlano, Justin, Tolomeo, Leonardo
We consider the stochastic damped nonlinear wave equation $\partial_t^{2}u+\partial_t u+u-\Delta u +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} \xi$ on the two-dimensional torus $\mathbb T^2$, where $\xi$ denotes a space-time white noise and $s>0$
Externí odkaz:
http://arxiv.org/abs/2409.20451
In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional un
Externí odkaz:
http://arxiv.org/abs/2403.06554
We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real line with initial data distributed according to Gibbs measure. We also prove that Gibbs measure is invariant under these dynamics. On the way, we provide a new pro
Externí odkaz:
http://arxiv.org/abs/2401.04292
We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any depth parameter, by establish
Externí odkaz:
http://arxiv.org/abs/2311.08142
Autor:
Chapouto, Andreia, Forlano, Justin
We consider the real-valued defocusing modified Korteweg-de Vries equation (mKdV) on the circle. Based on the complete integrability of mKdV, Killip-Vi\c{s}an-Zhang (2018) discovered a conserved quantity which they used to prove low regularity a prio
Externí odkaz:
http://arxiv.org/abs/2305.14565
Autor:
Chapouto, Andreia1 (AUTHOR), Forlano, Justin1 (AUTHOR), Li, Guopeng2 (AUTHOR), Oh, Tadahiro1 (AUTHOR), Pilod, Didier3 (AUTHOR)
Publikováno v:
Proceedings of the American Mathematical Society, Series B. 9/12/2024, Vol. 11, p452-468. 17p.
Autor:
Forlano, Justin
We study the real-valued modified KdV equation on the real line and the circle, in both the focusing and the defocusing case. By employing the method of commuting flows introduced by Killip and Vi\c{s}an (2019), we prove global well-posedness in $H^{
Externí odkaz:
http://arxiv.org/abs/2205.13110
Autor:
Forlano, Justin, Tolomeo, Leonardo
We consider the Cauchy problem for the fractional nonlinear Schr\"{o}dinger equation (FNLS) on the one-dimensional torus with cubic nonlinearity and high dispersion parameter $\alpha > 1$, subject to a Gaussian random initial data of negative Sobolev
Externí odkaz:
http://arxiv.org/abs/2205.11453
Autor:
Forlano, Justin, Seong, Kihoon
We study the transport property of Gaussian measures on Sobolev spaces of periodic functions under the dynamics of the one-dimensional cubic fractional nonlinear Schr\"{o}dinger equation. For the case of second-order dispersion or greater, we establi
Externí odkaz:
http://arxiv.org/abs/2102.13398
Autor:
Forlano, Justin, Tolomeo, Leonardo
We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the $2$-dimensional torus. The noise is taken to be slightly more regular than space-time white noise. In t
Externí odkaz:
http://arxiv.org/abs/2102.09075