Plausible Structures for 2-D Euler Systems

2001 ◽  
pp. 195-210
Author(s):  
Yuxi Zheng
Keyword(s):  
Euler Systems

scholarly journals The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier–Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1195
Author(s):  
Shu Wang ◽  
Yongxin Wang
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Large Amplitude ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Well Posedness ◽  
Spherical Coordinates ◽  
Smooth Solutions ◽  
Euler Systems

This paper investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the three-dimensional (3D) incompressible Navier–Stokes (NS) and Euler systems. The global well-posedness for large amplitude smooth solutions to the Cauchy problem for 3D incompressible NS and Euler equations based on a class of variant spherical coordinates is obtained, where smooth initial data is not axi-symmetric with respect to any coordinate axis in Cartesian coordinate system. Furthermore, we establish the existence, uniqueness and exponentially decay rate in time of the global strong solution to the initial boundary value problem for 3D incompressible NS equations for a class of the smooth large initial data and a class of the special bounded domain described by variant spherical coordinates.

scholarly journals Geometric Euler systems for locally isotropic motives

2004 ◽  
Vol 140 (02) ◽  
pp. 317-332 ◽  
Author(s):  
Tom Weston
Keyword(s):  
Euler Systems

scholarly journals Stability of a Kirchhoff–Roe scheme for two-dimensional linearized Euler systems

2017 ◽  
Vol 64 (2) ◽  
pp. 335-360 ◽  
Author(s):  
Emmanuel Franck ◽  
Laurent Gosse
Keyword(s):  
Two Dimensional ◽  
Euler Systems

scholarly journals Truncated Euler Systems over Imaginary Quadratic Fields

2009 ◽  
Vol 195 ◽  
pp. 97-111
Author(s):  
Soogil Seo
Keyword(s):  
Class Group ◽  
Quadratic Field ◽  
Abelian Extension ◽  
Iwasawa Theory ◽  
Quadratic Fields ◽  
Galois Module ◽  
Imaginary Quadratic Fields ◽  
Euler Systems ◽  
Graded Module ◽  
Elliptic Units

AbstractLet K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

Théorie d’Iwasawa des unités de Stark et groupe de classes

2017 ◽  
Vol 13 (05) ◽  
pp. 1165-1190 ◽  
Author(s):  
Jilali Assim ◽  
Youness Mazigh ◽  
Hassan Oukhaba
Keyword(s):  
Number Field ◽  
Finite Extension ◽  
Projective Limit ◽  
Ideal Class ◽  
Class Groups ◽  
Euler Systems ◽  
Ideal Class Groups ◽  
Stark Units ◽  
Characteristic Ideal ◽  
The Ideal

Let [Formula: see text] be a number field and let [Formula: see text] be an odd rational prime. Let [Formula: see text] be a [Formula: see text]-extension of [Formula: see text] and let [Formula: see text] be a finite extension of [Formula: see text], abelian over [Formula: see text]. In this paper we extend the classical results, e.g. [16], relating characteristic ideal of the [Formula: see text]-quotient of the projective limit of the ideal class groups to the [Formula: see text]-quotient of the projective limit of units modulo Stark units, in the non-semi-simple case, for some [Formula: see text]-irreductible characters [Formula: see text] of [Formula: see text]. The proof essentially uses the theory of Euler systems.

Euler Systems

2007 ◽  
pp. 435-483 ◽  
Author(s):  
V. A. Kolyvagin
Keyword(s):  
Euler Systems
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