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The Growth of Hypoelliptic Polynomials and Gevrey Classes [PDF]
Proceedings of the American Mathematical Society, 1973 For given hypoelliptic polynomials P P and
Newberger, E., Zielezny, Z.
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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.
Chao-Jiang Xu, Wei-Xi Li
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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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Gevrey Class Smoothing Effect for the Prandtl Equation [PDF]
SIAM Journal on Mathematical Analysis, 2016 It is well known that the Prandtl boundary layer equation is unstable for general initial data, and is well-posed in Sobolev space for monotonic initial data. Recently, under the Oleinik's monotonicity assumption for the initial datum, R. Alexandre, Y. Wang, C.-J. Xu, and T. Yang [J. Amer. Math. Soc., 28 (2015) pp.
Wei-Xi Li
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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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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
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Open Mathematics, 2020 Given the abstract evolution equation y′(t)=Ay(t),t∈ℝ,y^{\prime} (t)=Ay(t),t\in {\mathbb{R}}, with a scalar type spectral operator A in a complex Banach space, we find conditions on A, formulated exclusively in terms of the location of its spectrum in ...
Markin Marat V.
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Microhyperbolic Operators in Gevrey Classes
Publications of the Research Institute for Mathematical Sciences, 1989 This paper considers microhyperbolic operators in Gevrey classes and proves the microlocal well-posedness of the microlocal Cauchy problem. It also establishes theorems on the propagation of singularities for microhyperbolic operators. The methods show one how to obtain microlocal results (e.g.
Kajitani, Kunihiko +1 more
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Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator”
International Journal of Mathematics and Mathematical Sciences, 2018 The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space ...
Marat V. Markin
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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 ...
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