Results 21 to 30 of about 142 (127)
Mathematics, 2021 In this paper, we consider the generalized porous medium equation. For small initial data u0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using ...
Muhammad Zainul Abidin, Jiecheng Chen
doaj +1 more source
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
Long‐Time Instability of the Couette Flow in Low Gevrey Spaces
Communications on Pure and Applied Mathematics, Volume 76, Issue 10, Page 2804-2887, October 2023., 2023 Abstract We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2.
Yu Deng, Nader Masmoudi
wiley +1 more source
An interpolation problem in the Denjoy–Carleman classes
Mathematische Nachrichten, Volume 296, Issue 3, Page 902-914, March 2023., 2023 Abstract Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real‐analytic coefficients, we consider the following question. Given a smooth function defined on [a,b]⊂R$[a,b]\subset {\mathbb {R}}$ and given an increasing divergent sequence ...
Paolo Albano, Marco Mughetti
wiley +1 more source
Abstract and Applied Analysis, Volume 2023, Issue 1, 2023., 2023 We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of Fuchsian type in time t and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on ...
Stéphane Malek, Ying Hu
wiley +1 more source
A Paley–Wiener theorem in extended Gevrey regularity [PDF]
Journal of Pseudo-Differential Operators and Applications, 2019 In this paper we introduce appropriate associated function to the sequence $M_p=p^{\t p^{\s}}$, $p\in \N$, $\t>0$, $\s>1$, and derive its sharp asymptotic estimates in terms of the Lambert $W$ function. These estimates are used to prove a Paley-Wiener type theorem for compactly supported functions from extended Gevrey classes.
Pilipović, Stevan +2 more
openaire +2 more sources
Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces
Mathematics, 2022 We are concerned with a system of equations governing the evolution of isothermal, viscous, and compressible fluids of the Korteweg type, which is used to describe a two-phase liquid–vapor mixture.
Zihao Song, Jiang Xu
doaj +1 more source
Propagation of Gevrey Regularity for a Class of Hypoelliptic Equations [PDF]
Transactions of the American Mathematical Society, 1996 We prove results on the propagation of Gevrey and analytic wave front sets for a class of C ∞
Bove, Antonio, Tartakoff, David S.
openaire +2 more sources
Solvability in Gevrey Classes of Some Nonlinear Fractional Functional Differential Equations
International Journal of Differential Equations, 2020 Our purpose in this paper is to prove, under some regularity conditions on the data, the solvability in a Gevrey class of bound −1 on the interval −1,1 of a class of nonlinear fractional functional differential equations.
Hicham Zoubeir
doaj +1 more source
On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols
Mathematics, 2020 In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion.
Alexandre Arias Junior, Marco Cappiello
doaj +1 more source