Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Didier Pilod"'
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 149:73-97
This paper focuses on the Dysthe equation which is a higher order approximation of the water waves system in the modulation (Schrodinger) regime and in the infinite depth case. We first review the derivation of the Dysthe and related equations. Then
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5ee42ad3de5d85c13efeebfec3b1c620
https://doi.org/10.1016/j.matpur.2020.11.001
https://doi.org/10.1016/j.matpur.2020.11.001
Autor:
Didier Pilod, Yvan Martel
Publikováno v:
Communications in Mathematical Physics
For the mass critical generalized KdV equation $\partial_t u + \partial_x (\partial_x^2 u + u^5)=0$ on $\mathbb R$, we construct a full family of flattening solitary wave solutions. Let $Q$ be the unique even positive solution of $Q''+Q^5=Q$. For any
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86e6cd15d0b867529d408d8c3eebd8bd
https://doi.org/10.1007/s00220-020-03815-z
https://doi.org/10.1007/s00220-020-03815-z
Autor:
Didier Pilod, Henrik Kalisch
Publikováno v:
Proceedings of the American Mathematical Society. 147:2545-2559
In this note, we prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions. Those systems can be seen as a weak nonlocal dispersive perturbation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bd25705c1696b4115fb85fe49d117c2a
https://doi.org/10.1090/proc/14397
https://doi.org/10.1090/proc/14397
Publikováno v:
Journal of Mathematical Fluid Mechanics
We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev-Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev-Petviashvili equations. The proof of these estimates combines
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::411ecf8200092a39a445e6f7587ccf3a
http://arxiv.org/abs/2005.08789
http://arxiv.org/abs/2005.08789
Publikováno v:
Communications in Partial Differential Equations
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if $u_1,\,u_2$ are two suitable solutions of the equation defined in $\mathbb R^n\times[0,T]$ such that for s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6783dc28f1e4b552b21a9114e3088759
https://hdl.handle.net/11250/2766909
https://hdl.handle.net/11250/2766909
Publikováno v:
Revista Matemática Iberoamericana. 34:1563-1608
We prove that the modified Korteweg–de Vries (mKdV) equation is unconditionally well-posed in Hs(R) for s>1/3. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the constructio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dff9ac28324846858a0a9651d35363dc
https://doi.org/10.4171/rmi/1036
https://doi.org/10.4171/rmi/1036
Publikováno v:
SIAM Journal on Mathematical Analysis. 50:3172-3209
The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev-Petviashvili (KP) equations including the KP version of the Benjamin-Ono and Intermediate Long Wave
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::493ca4a1ea77f9e8469baae9f3ef2c40
https://doi.org/10.1137/17m1145379
https://doi.org/10.1137/17m1145379
Publikováno v:
Studies in Applied Mathematics. 140:133-177
The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular, we establish rigorous bounds between solutions of the Whitham and Korteweg–de Vries equations and p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::445e6d9051df668aa3e55cef66cb00dd
https://doi.org/10.1111/sapm.12194
https://doi.org/10.1111/sapm.12194
Publikováno v:
J. Math. Soc. Japan 71, no. 1 (2019), 147-201
We prove that the modified Korteweg–de Vries equation is unconditionally well-posed in $H^s({\mathbb{T}})$ for $s\ge 1/3$. For this we gather the smoothing effect first discovered by Takaoka and Tsutsumi with an approach developed by the authors th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d406aeae5598e0d7e8bc5b7206388eb
https://doi.org/10.2969/jmsj/76977697
https://doi.org/10.2969/jmsj/76977697
Autor:
Didier Pilod
Publikováno v:
Séminaire Laurent Schwartz — EDP et applications. :1-12
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::12a5b760b0ebd1d8266107e021611e2a
https://doi.org/10.5802/slsedp.73
https://doi.org/10.5802/slsedp.73