Results 11 to 20 of about 3,445 (164)
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
Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations [PDF]
, 2015 We consider the incompressible Euler equations on ${\mathbb R}^d$, where $d \in \{ 2,3 \}$. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey ...
Constantin, Peter +2 more
core +2 more sources
Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Advanced Nonlinear Studies, 2018 This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
doaj +1 more source
Counterexamples to $ C^{\infty} $ well posedness for some hyperbolic operators with triple characteristics [PDF]
, 2014 In this paper we prove that for a class of non-effectively hyperbolic operators with smooth triple characteristics the Cauchy problem is well posed in the Gevrey 2 class, beyond the generic Gevrey class $ 3/2 $ (see e.g. \cite{Bro}).
Bernardi, Enrico, Nishitani, Tatsuo
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Gevrey Hypoellipticity for a Class of Kinetic Equations [PDF]
Communications in Partial Differential Equations, 2011 In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
openaire +4 more sources
Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations [PDF]
, 2014 In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space.
Hao, Jianghao +2 more
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Gevrey class regularity for parabolic equations
Differential and Integral Equations, 2001 We consider the regularity of parabolic equations. We obtain that the solution belongs to Gevrey class 2 up to the boundary if functions in the equation belong to Gevrey class 2 in all dependent variables.
Lee, Pei-Ling, Guo, Yung-Jen Lin
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Bruno Pini Mathematical Analysis Seminar, 2015 In this article, we show that under some coercive assumption on the complex-valued potential V(x), the derivatives of the resolvent of the non-selfadjoint Schröinger operator H = −∆ + V(x) satisfy some Gevrey estimates at the threshold zero.
Xue Ping Wang
doaj +1 more source
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation [PDF]
, 2009 In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time.
Lekrine, Nadia, Xu, Chao-Jiang
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Eigenfunction expansions of ultradifferentiable functions and ultradistributions [PDF]
, 2016 In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$.
Dasgupta, Aparajita, Ruzhansky, Michael
core +3 more sources