Zobrazeno 1 - 10
of 625
pro vyhledávání: '"Gerard, Patrick"'
Truth Social, launched as a social media platform with a focus on free speech, has become a prominent space for political discourse, attracting a user base with diverse, yet often conservative, viewpoints. As an emerging platform with minimal content
Externí odkaz:
http://arxiv.org/abs/2411.01330
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^2(\mathbb{R})$ is obtained explicitly for generic rational initial data $u_0$. An explicit asymptotic wave profile $u^\mathr
Externí odkaz:
http://arxiv.org/abs/2410.17405
We show that the initial-value problem for the Benjamin-Ono equation on $\mathbb{R}$ with $L^2(\mathbb{R})$ rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The dimension
Externí odkaz:
http://arxiv.org/abs/2410.14870
Fear and Loathing on the Frontline: Decoding the Language of Othering by Russia-Ukraine War Bloggers
Othering, the act of portraying outgroups as fundamentally different from the ingroup, often escalates into framing them as existential threats--fueling intergroup conflict and justifying exclusion and violence. These dynamics are alarmingly pervasiv
Externí odkaz:
http://arxiv.org/abs/2409.13064
Following the Russian Federation's full-scale invasion of Ukraine in February 2022, a multitude of information narratives emerged within both pro-Russian and pro-Ukrainian communities online. As the conflict progresses, so too do the information narr
Externí odkaz:
http://arxiv.org/abs/2409.07684
One of the primary impediments hindering the widespread acceptance of autonomous vehicles (AVs) among pedestrians is their limited comprehension of AVs. This study employs virtual reality (VR) to provide pedestrians with an immersive environment for
Externí odkaz:
http://arxiv.org/abs/2401.02339
Autor:
Bambusi, Dario, Gérard, Patrick
We consider a perturbation of the Benjamin Ono equation with periodic boundary conditions on a segment. We consider the case where the perturbation is Hamiltonian and the corresponding Hamiltonian vector field is analytic as a map form energy space t
Externí odkaz:
http://arxiv.org/abs/2312.02833
Autor:
Gérard, Patrick, Topalov, Peter
In this paper we prove that the Benjamin-Ono equation is globally in time $C^0$-well-posed in the Hilbert space $H^{-1/2,\sqrt{\log}}(\mathbb{T},\mathbb{R})$ of periodic distributions in $H^{-1/2}(\mathbb{T},\mathbb{R})$ with $\sqrt{\log}$-weights. T
Externí odkaz:
http://arxiv.org/abs/2308.07829
Autor:
Gérard, Patrick
We identify the zero dispersion limit of a solution of the Benjamin--Ono equation on the line corresponding to every initial datum in $L^2(\R)\cap L^\infty(\R )$. We infer a maximum principle and a local smoothing property for this limit. The proof i
Externí odkaz:
http://arxiv.org/abs/2307.12768
Autor:
Gérard, Patrick, Pushnitski, Alexander
We establish an explicit formula for the solution of the the cubic Szeg\H{o} equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class $H^2$ on the real line
Externí odkaz:
http://arxiv.org/abs/2307.06734