Results 121 to 130 of about 3,682,860 (177)

Strong hyperbolicity in Gevrey classes

Journal of Differential Equations, 2021
In this paper, the authors consider the Cauchy problem \[ \begin{cases} P(t,\partial_t,\partial_x)u(t,x)=0,\quad(t,x)\in[0,T]\times\mathbb R\\ \partial_t^ju(0,x)=u_j(x),\quad x\in\mathbb R,\quad j=0,...,m-1 \end{cases}\tag{CP} \] where \(P\) is a differential operator of order \(m\) with respect to \(t\) written in the form \[P(t,\partial_t,\partial_x)=
F. Colombini, N. Orrú, G. Taglialatela
semanticscholar   +4 more sources

Hypoellipticity and Local Solvability in Gevrey Classes

Mathematische Nachrichten, 2002
As standard, let \(G^s ...
A. Albanese, A. Corli, L. Rodino
semanticscholar   +6 more sources

Cauchy Problem in the Gevrey Classes

, 2017
In Chap. 6 we showed that there exists a second order differential operator of spectral type 2 on Σ with bicharacteristics tangent to the double characteristic manifold for which the Cauchy problem is ill-posed in the Gevrey class of order s for any s > 5 even though the Levi condition is satisfied.
T. Nishitani
semanticscholar   +2 more sources

FBI transforms in Gevrey classes

Journal d'Analyse Mathématique, 1997
The following theorem is proved: Let \({\mathcal O}\) be a Gevrey \(s\) strictly convex obstacle, \(1 \leq s < 3\). Then for every positive \(\varepsilon\) there are only finitely many resonances in the region \(\{ k \in {\mathbb C} \mid\text{Re }k \geq 1, \text{ Im } k \geq -(C_{0, a} - \varepsilon) (\text{Re } k)^{1/3} \}\).
B. Lascar, R. Lascar
semanticscholar   +3 more sources

Regularly hyperbolic systems and Gevrey classes

Annali di Matematica Pura ed Applicata, 1985
This paper deals with the first order Cauchy problem \[ (1)\quad \partial U/\partial t=\sum A_ h(t,x) \partial U/\partial x_ h+B(t,x),\quad U(0,x)=g(x), \] \(0\leq t\leq T\), \(x\in {\mathbb{R}}^ n\), where \(A_ h\) (1\(\leq h\leq n)\) and \(B\) are \(N\times N\) real matrices, while U and g are real \(N\)-vectors. System (1) is assumed to be regularly
E. Jannelli
semanticscholar   +2 more sources

Long‐Time Instability of the Couette Flow in Low Gevrey Spaces

Communications on Pure and Applied Mathematics, 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
exaly   +2 more sources

Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes

Journal of Differential Equations, 2019
A. Biswas and J. Hudson are partially supported by NSF grant DMS-1517027. J. Tian is partially supported by the AMS Simons Travel Grant.
A. Biswas, Joshua Hudson, Jing Tian
semanticscholar   +1 more source

On the solvability of the Cauchy problem in Gevrey classes for the equation with Weyl fractional derivative

Uzbek Mathematical Journal
A new representation of fractional-order Weyl derivatives is given. The Cauchy problem is studied for partial differential equations containing Weyl derivatives. The conditions under which this problem has solutions from the Gevrey classes are found.
S. Alimov
semanticscholar   +1 more source

ON THE SOLVABILITY OF THE CAUCHY PROBLEM IN GEVREY CLASSES FOR THE WEYL FRACTIONAL DERIVATIVE EQUATION

Доклады Российской академии наук. Математика, информатика, процессы управления / Doklady Mathematics
An alternative definition of fractional-order Weyl derivatives is given and their effect on functions from the Gevrey classes is studied. Conditions for the solvability of the Cauchy problem in Gevrey classes are found for the Weyl partial differential ...
S. Alimov
semanticscholar   +1 more source

The Cauchy problem for p-evolution equations with variable coefficients in Gevrey classes

Evolution Equations and Control Theory
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we prove
Alexandre Arias Junior, A. Ascanelli, M. Cappiello, Eliakim Cleyton Machado   +3 more
semanticscholar   +1 more source