Results 11 to 20 of about 2,438 (123)
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
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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
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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
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Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In this paper, we work on the Cauchy problem of the three‐dimensional micropolar fluid equations. For small initial data, in the variable‐exponent Fourier–Besov spaces, we achieve the global well‐posedness result. The Littlewood–Paley decomposition method and the Fourier‐localization technique are main tools to obtain the results. Moreover, the results
Muhammad Zainul Abidin +4 more
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Viscosity Limits for Zeroth‐Order Pseudodifferential Operators
Communications on Pure and Applied Mathematics, Volume 75, Issue 8, Page 1798-1869, August 2022., 2022 Abstract Motivated by the work of Colin de Verdière and Saint‐Raymond on spectral theory for zeroth‐order pseudodifferential operators on tori, we consider viscosity limits in which zeroth‐order operators, P, are replaced by P + iν Δ, ν > 0. By adapting the Helffer–Sjöstrand theory of scattering resonances, we show that, in a complex neighbourhood of ...
Jeffrey Galkowski, Maciej Zworski
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Finite‐time local piecewise control for parabolic PDEs with ODE output feedback
IET Control Theory &Applications, Volume 16, Issue 2, Page 229-243, January 2022., 2022 Abstract This paper is devoted to the finite‐time local piecewise control for parabolic partial differential equations (PDEs) by using dynamic output feedback control strategy, where the controller is designed as an ordinary differential equation (ODE).
Manna Li, Weijie Mao
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Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The main aim of this survey article is to present several known results about vector‐valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables.
Wei-Shih Du +3 more
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Multi-Anisotropic Gevrey Regularity of Hypoelliptic Operators [PDF]
, 2008 This is the preprint version of our paper in the journal Operator Theory : Advances and Applications, Vol.
Bouzar, Chikh, Dali, Ahmed
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Global Well‐Posedness for Coupled System of mKdV Equations in Analytic Spaces
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 The main result in this paper is to prove, in Bourgain type spaces, the existence of unique local solution to system of initial value problem described by integrable equations of modified Korteweg‐de Vries (mKdV) by using linear and trilinear estimates, together with contraction mapping principle. Moreover, owing to the approximate conservation law, we
Khaled Zennir +3 more
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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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