Results 31 to 40 of about 142 (127)
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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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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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
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Gevrey regularity and analyticity for the modified Camassa–Holm equation [PDF]
Journal of Nonlinear Mathematical Physics, 2022 AbstractThis paper deals with the analyticity and Gevrey regularity for the Cauchy problem of a modified Camassa–Holm (mCH) equation in Sobolev–Gevrey space $$G_{r,s}^\delta$$ G r , s δ
Zhou, Qingyu +2 more
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Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity
Abstract and Applied Analysis, 2014 The Cauchy problem of the nonlinear spatially homogeneous Boltzmann equation without angular cutoff is studied. By using analytic techniques, one proves the Gevrey regularity of the C∞ solutions in non-Maxwellian and strong singularity cases.
Shi-you Lin
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Gevrey class regularity for analytic differential-delay equations
Electronic Journal of Qualitative Theory of Differential Equations, 2016 This paper considers differential-delay equations of the form \[x'(t)=p(t)x(t-1),\] where the coefficient function $p\colon\mathbb{R}\rightarrow\mathbb{C}$ is analytic and not bounded on any $\delta$-neighborhood of the intervals $\left(-\infty,\gamma ...
Roger Nussbaum, Gabriella Vas
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Multi-Anisotropic Gevrey Regularity of Hypoelliptic Operators [PDF]
, 2008 We show a multi-anisotropic Gevrey regularity of solutions of hypoelliptic equations.
Bouzar, Chikh, Dali, Ahmed
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On the sharp Gevrey regularity for a generalization of the Métivier operator
Mathematische Annalen, 2023 The sharp Gevrey hypoellipticity is provided for the following generalization of the Métivier operator, "Non-hypoellipticité analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D_{y}^{2}$" by G. Métivier, \begin{align*} D_{x}^{2}+\left(x^{2n+1}D_{y}\right)^{2}+\left(x^{n}y^{m}D_{y}\right)^{2}, \end{align*} in $Ω$ open neighborhood of the origin in ...
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Dissipativity and Gevrey regularity of a Smoluchowski equation [PDF]
Indiana University Mathematics Journal, 2005 Summary: We investigate a Smoluchowski equation (a nonlinear Fokker-Planck equation on the unit sphere), which arises in modeling of colloidal suspensions. We prove the dissipativity of the equation in 2D and 3D, in certain Gevrey classes of analytic functions.
Constantin, Peter +2 more
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Beyond gevrey regularity: Superposition and propagation of singularities
Filomat, 2018 We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well.
Pilipović, Stevan +2 more
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