Results 11 to 20 of about 157 (145)
Communications on Pure and Applied Mathematics, Volume 76, Issue 12, Page 3685-3768, December 2023., 2023 Abstract We investigate the long‐time properties of the two‐dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical Miles‐Howard stability condition on the Richardson number, we prove that the system experiences a shear‐buoyancy instability: the density variation
Jacob Bedrossian +3 more
wiley +1 more source
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)}.
CHEN H., RODINO, Luigi Giacomo
openaire +3 more sources
Inhomogeneous Gevrey classes and ultradistributions
Journal of Mathematical Analysis and Applications, 2004 Starting from the definition of inhomogeneous Gevrey classes given by \textit{O. Liess} and \textit{L. Rodino} [Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 3, 233--323 (1984; Zbl 0557.35131)], the authors introduce the non-quasi-analytic inhomogeneous Gevrey classes of Roumieu type, denoted by \(G^{s, \lambda}.\) Such a class of ...
D. Calvo +2 more
openaire +4 more sources
The Growth of Hypoelliptic Polynomials and Gevrey Classes [PDF]
Proceedings of the American Mathematical Society, 1973 For given hypoelliptic polynomials P P and Q Q , classes Γ P ρ ( Ω ) \Gamma _P^\rho (\Omega ) and Γ Q ρ ( Ω ) \Gamma _Q^\rho (\Omega ) involving Gevrey type ...
Newberger, E., Zielezny, Z.
openaire +1 more source
Gevrey class regularity of the magnetohydrodynamics equations [PDF]
The ANZIAM Journal, 2002 AbstractIn this article, we use the method of Foias and Temam to show that the strong solutions of the time-dependent magnetohydrodynamics equations in a periodic domain are analytic in time with values in a Gevrey class of functions. As immediate corollaries we find that the solutions are analytic in Hr-norms and that the solutions become smooth ...
openaire +2 more sources
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 +2 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
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 +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
Newton Polygons and Formal Gevrey Classes
Publications of the Research Institute for Mathematical Sciences, 1990 Untersucht wird ein Cauchyproblem \(Pu=f(t,x)\), \(D^ j_ tu|_{t=0}=g_ j\) (0\(\leq j\leq m-1)\) wobei P die Form hat \(P=D_ t^ m+\sum_{0\leq jm\) ist. Hierzu existiert eine eindeutige Lösung \(u\in G^{\infty}\), nämlich als eine formale Potenzreihe. Gezeigt wird: es ist \(u\in G^ s\) mit \(s=1+1/k_ 1\).
openaire +3 more sources