Results 1 to 10 of about 518 (155)
Extended Gevrey Regularity via Weight Matrices
Axioms, 2022 The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces Gt(U) and the space of smooth functions C∞(U). The first approach in the style of Komatsu is based on the properties of two
Nenad Teofanov, Filip Tomić
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Journal of Mathematics, 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.
Muhammad Zainul Abidin +3 more
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A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process
Comptes Rendus. Mathématique, 2022 In this short note we capitalize on and complete our previous results on the regularity of the homogenized coefficients for Bernoulli perturbations by addressing the case of the Poisson point process, for which the crucial uniform local finiteness ...
Duerinckx, Mitia, Gloria, Antoine
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On the regularity of the solutions and of analytic vectors for “sums of squares”
Bruno Pini Mathematical Analysis Seminar, 2023 We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type.
Gregorio Chinni
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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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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
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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
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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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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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