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of 52
pro vyhledávání: '"Vento, Stéphane"'
We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation $$ u_t+D^\alpha u_x + u^p u_x= 0, \quad 1<\alpha\le 2, \quad p\in {\mathbb N}\setminus\{0\}, $$ with homogeneous initial data $\Phi$. We show that, under smallne
Externí odkaz:
http://arxiv.org/abs/2410.12063
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
Externí odkaz:
http://arxiv.org/abs/1702.03191
We prove that the modified KdV equation is unconditionally well-posed in H s (T) for s $\ge$ 1/3.
Comment: We corrected a flaw in the definition of the extension operator (Page 13) kindly indicated to us by Professor Tsutsumi. Corrected version
Comment: We corrected a flaw in the definition of the extension operator (Page 13) kindly indicated to us by Professor Tsutsumi. Corrected version
Externí odkaz:
http://arxiv.org/abs/1607.05483
Autor:
Ribaud, Francis, Vento, Stéphane
We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation$$ u\_t-D\_x^\alpha u\_{x} + u\_{xyy} = uu\_x,\quad (t,x,y)\in\R^3,\quad 1\le \alpha\le 2,$$is locally well-posed in the spaces $E
Externí odkaz:
http://arxiv.org/abs/1601.00856
We prove that the modified Korteweg- de Vries equation (mKdV) equation is unconditionally well-posed in $H^s(\mathbb R)$ for $s> \frac 13$. Our method of proof combines the improvement of the energy method introduced recently by the first and third a
Externí odkaz:
http://arxiv.org/abs/1411.5707
Autor:
Vento, Stéphane
Dans cette thèse nous nous intéressons aux propriétés qualitatives et quantitatives des solutions de quelques équations d'ondes en milieux dispersifs ou dispersifs-dissipatifs. Dans une première partie, nous étudions le problème de Cauchy ass
Externí odkaz:
http://www.theses.fr/2008PEST0261/document
Autor:
Molinet, Luc, Vento, Stéphane
Publikováno v:
Anal. PDE 8 (2015) 1455-1495
In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below $ H^1 $ for a
Externí odkaz:
http://arxiv.org/abs/1409.4525
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 determined. A consequence of this study is the existence of classes of smooth, complex--valued solutions of this
Externí odkaz:
http://arxiv.org/abs/1201.0442
Autor:
Vento, Stéphane, Ribaud, Francis
In this note we study the generalized 2D Zakharov-Kuznetsov equations $\partial_tu+\Delta\partial_xu+u^k\partial_xu=0$ for $k\ge 2$. By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces $H^s(\mathbb{R}^2)$
Externí odkaz:
http://arxiv.org/abs/1111.4384
Autor:
Ribaud, Francis, Vento, Stéphane
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 $H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$. The proof is based on a
Externí odkaz:
http://arxiv.org/abs/1111.2850