Results 31 to 40 of about 429 (166)

Paradifferential calculus in Gevrey classes

Kyoto Journal of Mathematics, 2001
The paper presents a paradifferential calculus adapted to the study of nonlinear partial differential equations in Gevrey classes. Namely, in the second section of the paper the authors consider Gevrey-Sobolev spaces \(H^s_{\lambda,\sigma}\) defined by the norms \[ \biggl \|\exp \bigl(\lambda |D|^{1/ \sigma}\bigr)u \biggr\|_{H^s(\mathbb{R}^n)}.
Hua, Chen, Rodino, Luigi
openaire   +2 more sources

Propagation des singularités Gevrey pour l'équation de Cauchy-Riemann dégénérée [PDF]

, 2001
International audienceIn this paper we study the degenerate Cauchy-Riemann equation in Gevrey classes. We first prove the local solvability in Gevrey classes of functions and ultra-distributions.
Lerner, Nicolas, Lascar, Bernard
core   +1 more source

On the stability of vacuum in the screened Vlasov–Poisson equation

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract We study the asymptotic behavior of small data solutions to the screened Vlasov–Poisson equation on Rd×Rd$\mathbb {R}^d\times \mathbb {R}^d$ near vacuum. We show that for dimensions d⩾2$d\geqslant 2$, under mild assumptions on localization (in terms of spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions ...
Mikaela Iacobelli, Stefano Rossi, Klaus Widmayer   +2 more
wiley   +1 more source

On the global $C^\infty$ and Gevrey hypoellipticity on the torus of some classes of degenerate elliptic operators [PDF]

, 2011
In this paper we prove the global $C^\infty$ and Gevrey hypoellipticity on the multidimensional torus for some classes of degenerate elliptic ...
ALBANESE, Angela Anna, Albanese, Angela A.   +1 more
core   +1 more source

New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in
Tegegne Getachew, Xiasheng Shi
wiley   +1 more source

Gevrey Regularity and Local Well-Posedness for the HirotaSatsuma System

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this paper, we examine the local well-posedness of the initial value problem for the HirotaSatsuma system within Gevrey spaces. This system, which consists of a coupled nonlinear dispersive partial differential equation, models the interactions ...
Boudersa Feriel, Mennouni Abdelaziz, Agarwal Ravi P.   +2 more
doaj   +1 more source

Global Solvability of the Generalized Navier−Stokes System in Critical Besov Spaces

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper is devoted to the global solvability of the Navier−Stokes system with a fractional Laplacian (−Δ)α in Rn for n ≥ 2, where the convective term has the form (|u|m−1u)·∇u for m ≥ 1. By establishing the estimates for the difference u1m−1u1−u2m−1u2 in homogeneous Besov spaces and employing the maximal regularity property of (−Δ)α in Lorentz−Besov
Huiyang Zhang, Shiwei Cao, Qinghua Zhang, Dengfeng Lu   +3 more
wiley   +1 more source

Partial hyperbolicity and partial gevrey classes

Journal of Differential Equations, 1981
Let P(D) be a linear partial differential operator of order m > 0 with constant coefficients in R” + ‘. Let d = (d,, d, ,..., d,) E R”+ i, 0 0 be an integer.
openaire   +1 more source

Evaluating Environmental Predictors of Fish Community Composition in a Semi‐Arid River System Using a Model‐Based Approach

Ecology of Freshwater Fish, Volume 34, Issue 3, July 2025.
ABSTRACT Understanding how the environment shapes species distribution and affects biodiversity patterns is important in ecology and conservation. Environmental stressors like climate change and anthropogenic impacts may lead to a significant decline in aquatic biodiversity.
Mojgan Zare Shahraki, Pejman Fathi, Sami Domisch, Andreas Bruder, Eisa Ebrahimi Dorcheh, Alireza Esmaeili Ofogh, Thomas Mehner   +6 more
wiley   +1 more source

Improved Gevrey‐1 Estimates of Formal Series Expansions of Center Manifolds

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT In this paper, we show that the coefficients ϕn$\phi _n$ of the formal series expansions ∑n=1∞ϕnxn∈xC[[x]]$\sum _{n=1}^\infty \phi _n x^n\in x\mathbb {C}[[x]]$ of center manifolds of planar analytic saddle‐nodes grow like Γ(n+a)$\Gamma (n+a)$ (after rescaling x$x$) as n→∞$n\rightarrow \infty$.
Kristian Uldall Kristiansen
wiley   +1 more source