scholarly journals Subelliptic Gevrey spaces

2020 ◽  
Author(s):  
Véronique Fischer ◽  
Michael Ruzhansky ◽  
Chiara Alba Taranto
Keyword(s):  
Gevrey Spaces

scholarly journals Microlocal smoothing effect for Schrödinger equations in Gevrey spaces

2003 ◽  
Vol 55 (4) ◽  
pp. 855-896 ◽  
Author(s):  
Kunihiko KAJITANI ◽  
Giovanni TAGLIALATELA
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Smoothing Effect ◽  
Gevrey Spaces

scholarly journals Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces

2021 ◽  
Vol 275 ◽  
pp. 234-249
Author(s):  
Daniel Oliveira da Silva ◽  
Alejandro J. Castro
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Well Posedness ◽  
Gevrey Spaces

scholarly journals Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space

1994 ◽  
Vol 135 ◽  
pp. 165-196 ◽  
Author(s):  
Masatake Miyake ◽  
Masafumi Yoshino
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Newton Polygon ◽  
Index Theorem ◽  
Fredholm Property ◽  
Goursat Problem ◽  
Point Of View ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Gevrey Spaces

In the study of ordinary differential equations, Malgrange ([Ma]) and Ramis ([R1], [R2]) established index theorem in (formal) Gevrey spaces, and the notion of irregularity was nicely defined for the study of irregular points. In their studies, a Newton polygon has a great advantage to describe and understand the results in visual form. From this point of view, Miyake ([M2], [M3], [MH]) studied linear partial differential operators on (formal) Gevrey spaces and proved analogous results, and showed the validity of Newton polygon in the study of partial differential equations (see also [Yn]).

A Result on Strong Uniqueness in Gevrey Spaces for Some Elliptic Operators

2005 ◽  
Vol 30 (1-2) ◽  
pp. 39-57 ◽  
Author(s):  
F. COLOMBINI ◽  
C. GRAMMATICO
Keyword(s):  
Elliptic Operators ◽  
Strong Uniqueness ◽  
Gevrey Spaces

scholarly journals Asymptotic expansion in Gevrey spaces for solutions of Navier–Stokes equations

2017 ◽  
Vol 104 (3-4) ◽  
pp. 167-190 ◽  
Author(s):  
Luan T. Hoang ◽  
Vincent R. Martinez
Keyword(s):  
Asymptotic Expansion ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gevrey Spaces

scholarly journals MICROLOCAL SMOOTHING EFFECT FOR SCHRÖDINGER EQUATIONS IN GEVREY SPACES

2003 ◽  
Author(s):  
KUNIHIKO KAJITANI ◽  
GIOVANNI TAGLIALATELA
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Smoothing Effect ◽  
Gevrey Spaces

scholarly journals Continuity and Analyticity for the Generalized Benjamin–Ono Equation

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2435
Author(s):  
Xiaolin Pan ◽  
Bin Wang ◽  
Rong Chen
Keyword(s):  
Lower Bound ◽  
Type Theorem ◽  
Well Posedness ◽  
Hölder Continuous ◽  
Solution Map ◽  
Gevrey Regularity ◽  
Gevrey Spaces ◽  
The Stability ◽  
Uniformly Continuous ◽  
Bo Equation

This work mainly focuses on the continuity and analyticity for the generalized Benjamin–Ono (g-BO) equation. From the local well-posedness results for g-BO equation, we know that its solutions depend continuously on their initial data. In the present paper, we further show that such dependence is not uniformly continuous in Sobolev spaces Hs(R) with s>3/2. We also provide more information about the stability of the data-solution map, i.e., the solution map for g-BO equation is Hölder continuous in Hr-topology for all 0≤r<s with exponent α depending on s and r. Finally, applying the generalized Ovsyannikov type theorem and the basic properties of Sobolev–Gevrey spaces, we prove the Gevrey regularity and analyticity for the g-BO equation. In addition, by the symmetry of the spatial variable, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map.

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