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pro vyhledávání: '"Molinet, Luc"'
Autor:
Molinet, Luc, Talhouk, Raafat
The Boussinesq-Peregrine system is derived from the water waves system in presence of topographic variation under the hypothesis of shallowness and small amplitude regime. The system becomes significantly simpler (at least in the mathematical sens) u
Externí odkaz:
http://arxiv.org/abs/2406.04711
Autor:
Guo, Zihua, Molinet, Luc
We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in $H^{s,0}({\mathbb R}^2)$ for $s>3/4$ and unconditional global well-posedness in the energy space. We also prove the global existence of perturb
Externí odkaz:
http://arxiv.org/abs/2404.12364
This paper is devoted to the study of existence and properties of solitary waves of the Benjamin equation. The studied equation includes a parameter $\gamma$ in front of the Benjamin-Ono term. We show the existence, uniqueness, decay and orbital stab
Externí odkaz:
http://arxiv.org/abs/2404.04711
Autor:
Farah, Luiz Gustavo, Molinet, Luc
In this note, we prove the local well-posedness in the energy space of the $k$-generalized Zakharov-Kuznetsov equation posed on $ \R\times \T $ for any power non-linearity $ k\ge 2$. Moreover, we obtain global solutions under a precise smallness assu
Externí odkaz:
http://arxiv.org/abs/2306.07433
Autor:
Molinet, Luc, Tanaka, Tomoyuki
We improve our previous result [L. Molinet and T. Tanaka, Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations, J. Funct. Anal. 283 (2022), 109490] on the Cauchy problem for one dimensional dispersive equation
Externí odkaz:
http://arxiv.org/abs/2207.08725
In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of $u_{xxx}$ is positive and uniformly bounded away from the origin and that a primitive function of the r
Externí odkaz:
http://arxiv.org/abs/2108.11104
Autor:
Molinet, Luc, Tanaka, Tomoyuki
We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $ i |\xi|^\
Externí odkaz:
http://arxiv.org/abs/2105.08731
In this work, we revisit the study by M. E. Schonbek [11] concerning the problem of existence of global entropic weak solutions for the classical Boussinesq system, as well as the study of the regularity of these solutions by C. J. Amick [1]. We prop
Externí odkaz:
http://arxiv.org/abs/2001.11870
Autor:
Khorbatly, Bashar, Molinet, Luc
In this paper, we prove an orbital stability result for the Degasperis-Procesi peakon with respect to perturbations having a momentum density that is first negative and then positive. This leads to the orbital stability of the antipeakon-peakon profi
Externí odkaz:
http://arxiv.org/abs/1912.10895
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