Zobrazeno 1 - 10
of 12
pro vyhledávání: '"Stéphane Vento"'
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
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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:
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d406aeae5598e0d7e8bc5b7206388eb
https://doi.org/10.2969/jmsj/76977697
https://doi.org/10.2969/jmsj/76977697
We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin-Ono equation $\partial$\_t u -- D^$\alpha$\_x $\partial$\_x u = $\partial$\_x(u^2), 0 < $\alpha$ $\le$ 1, is locally
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b754a58a37537b5b7eb21fe015132c3
http://arxiv.org/abs/1702.03191
http://arxiv.org/abs/1702.03191
Autor:
Stéphane Vento, Francis Ribaud
Publikováno v:
Comptes Rendus Mathematique. 350:499-503
In this Note we study the generalized 2D Zakharov–Kuznetsov equations ∂ t u + Δ ∂ x u + u k ∂ x u = 0 for k ⩾ 2 . By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces H s ( R 2 ) for s > 1 / 4 i
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https://explore.openaire.eu/search/publication?articleId=doi_________::868fe9ebd5d9bb43f4f957fb2eed5a39
https://doi.org/10.1016/j.crma.2012.05.007
https://doi.org/10.1016/j.crma.2012.05.007
Autor:
Francis Ribaud, Stéphane Vento
Publikováno v:
SIAM Journal on Mathematical Analysis. 44:2289-2304
We prove the local well-posedness of the three-dimensional Zakharov--Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\mathbb{R}^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\mathbb{R}^3)$. The pro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f76c8705dc64a9caf55a29a33e0ea5c6
https://doi.org/10.1137/110850566
https://doi.org/10.1137/110850566
Autor:
Stéphane Vento
Publikováno v:
Asymptotic Analysis. 68:155-186
We study the large time behavior of solutions to the dissipative Korteweg-de Vries equations ut + uxxx + |D|αu + uux = 0 with 0 < α < 2. We find asymptotic expansions of the solution as t→∞ in various Sobolev norms.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::756f959a3046b326b1c011944b4cb32b
https://doi.org/10.3233/asy-2010-0988
https://doi.org/10.3233/asy-2010-0988
Autor:
Luc Molinet, Stéphane Vento
Publikováno v:
Anal. PDE 8, no. 6 (2015), 1455-1495
Analysis & PDE
Analysis & PDE, Mathematical Sciences Publishers, 2015, 8 (6), pp.1455-1495
Analysis & PDE
Analysis & PDE, Mathematical Sciences Publishers, 2015, 8 (6), pp.1455-1495
We propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly nonresonant dispersive equations. As an example, we obtain unconditional well-posedness of the Cauchy problem in the energy space for a large c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82a9d87dbbc2f76655d8f626e36dc232
https://projecteuclid.org/euclid.apde/1510843151
https://projecteuclid.org/euclid.apde/1510843151
The dynamics of the poles of the two--soliton solutions of the modified Korteweg--de Vries equation $$ u_t + 6u^2u_x + u_{xxx} = 0 $$ are investigated. A consequence of this study is the existence of classes of smooth, complex--valued solutions of th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18227719835e341506928a874adc1983
Autor:
Luc Molinet, Stéphane Vento
Publikováno v:
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2013, 365 (1), pp.123-141
Transactions of the American Mathematical Society, American Mathematical Society, 2013, 365 (1), pp.123-141
We prove that the KdV-Burgers equation is globally well-posed in H − 1 ( T ) H^{-1}(\mathbb {T}) with a solution-map that is analytic from H − 1 ( T ) H^{-1}(\mathbb {T}) to C ( [ 0 , T ] ; H − 1 ( T ) ) C([0,T];H^{-1}(\mathbb {T})) , whereas i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::926e1e5f03d77a540367c5bc7bd4a70b
http://arxiv.org/abs/1005.4805
http://arxiv.org/abs/1005.4805
Autor:
Stéphane Vento, Luc Molinet
Publikováno v:
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2011, 10 (3), pp.531-560
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2011, 10 (3), pp.531-560
We complete the known results on the local Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in $ H^{-1}(\R) $ with a solution-map that is analytic from $H^{-1}(\R) $ to $C([0,T];H^{-1}(\R))$ wh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9918ab4c4c99436ee185ec86154b8832
http://arxiv.org/abs/0911.5256
http://arxiv.org/abs/0911.5256