Zobrazeno 1 - 10
of 2 420
pro vyhledávání: '"35q53"'
Autor:
Robert, Tristan
In this work, we pursue our investigations on the Cauchy problem for a class of dispersive PDEs where a rough time coefficient is present in front of the dispersion. We show that if the PDE satisfies a strong non-resonance condition (Theorem 1.6), ev
Externí odkaz:
http://arxiv.org/abs/2410.23051
Autor:
Robert, Tristan
In this work, we study the Cauchy problem for a class of dispersive PDEs where a rough time coefficient is present in front of the dispersion. Under minimal assumptions on the occupation measure of this coefficient, we show that for the large class o
Externí odkaz:
http://arxiv.org/abs/2410.23038
We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by K
Externí odkaz:
http://arxiv.org/abs/2410.17846
Autor:
Curtin, Conor, Ivanov, Rossen
Publikováno v:
Wave Motion 129 (2024) 103343
The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends quadratic-ally on
Externí odkaz:
http://arxiv.org/abs/2410.15209
We give a simpler proof for the local well-posedness of the modified Korteweg-de Vries equations and modified Benjamin-Ono equation in $H^{\frac{1}{4}}(\mathbb{R})$ and $H^{\frac{1}{2}}(\mathbb{R})$, respectively. The proof is based on the Strichartz
Externí odkaz:
http://arxiv.org/abs/2410.13656
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 prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses the invers
Externí odkaz:
http://arxiv.org/abs/2409.14480
This study builds upon a model proposed by Joanny and collaborators that examines the dynamics of interfaces between two distinct cell populations, particularly during tumor growth in healthy tissues. This framework leads to the investigation of a ge
Externí odkaz:
http://arxiv.org/abs/2409.12607
We consider the Cauchy problem to the 3D fractional Schr\"odinger equation with quadratic interaction of $u\bar u$ type. We prove the global existence of solutions and scattering properties for small initial data. For the proof, one novelty is that w
Externí odkaz:
http://arxiv.org/abs/2409.10804
We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its complete integr
Externí odkaz:
http://arxiv.org/abs/2409.06905