Results 11 to 20 of about 3,471 (160)
On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations [PDF]
, 2010 We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey ...
Baouendi M S Goulaouic C +18 more
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Smooth Gevrey normal forms of vector fields near a fixed point [PDF]
, 2013 We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the "small divisors" are invisible either for the smooth linearization or normal form problem.
Stolovitch, Laurent
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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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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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Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation [PDF]
, 2009 In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time.
Lekrine, Nadia, Xu, Chao-Jiang
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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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Counterexamples to $ C^{\infty} $ well posedness for some hyperbolic operators with triple characteristics [PDF]
, 2014 In this paper we prove that for a class of non-effectively hyperbolic operators with smooth triple characteristics the Cauchy problem is well posed in the Gevrey 2 class, beyond the generic Gevrey class $ 3/2 $ (see e.g. \cite{Bro}).
Bernardi, Enrico, Nishitani, Tatsuo
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Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations [PDF]
, 2015 We consider the incompressible Euler equations on ${\mathbb R}^d$, where $d \in \{ 2,3 \}$. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey ...
Constantin, Peter +2 more
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Bruno Pini Mathematical Analysis Seminar, 2015 In this article, we show that under some coercive assumption on the complex-valued potential V(x), the derivatives of the resolvent of the non-selfadjoint Schröinger operator H = −∆ + V(x) satisfy some Gevrey estimates at the threshold zero.
Xue Ping Wang
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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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