Euler System for Perfect Incompressible Fluids

2011 ◽  
pp. 291-333
Author(s):  
Hajer Bahouri ◽  
Jean-Yves Chemin ◽  
Raphaël Danchin
Keyword(s):  
Euler System ◽  
Incompressible Fluids

scholarly journals Iwasawa Theory of Elliptic Modular Forms Over Imaginary Quadratic Fields at Non-ordinary Primes

2019 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Euler System ◽  
Base Change ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Selmer Groups ◽  
Imaginary Quadratic Fields ◽  
Elliptic Modular Form

AbstractThis article is a continuation of our previous work [7] on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formulate integral Iwasawa main conjectures at non-ordinary primes $p$ for suitable twists of the base change of a newform $f$ to an imaginary quadratic field $K$ where $p$ splits, over the cyclotomic ${\mathbb{Z}}_p$-extension, the anticyclotomic ${\mathbb{Z}}_p$-extensions (in both the definite and the indefinite cases) as well as the ${\mathbb{Z}}_p^2$-extension of $K$. In order to do so, we define Kobayashi–Sprung-style signed Coleman maps, which we use to introduce doubly signed Selmer groups. In the same spirit, we construct signed (integral) Beilinson–Flach elements (out of the collection of unbounded Beilinson–Flach elements of Loeffler–Zerbes), which we use to define doubly signed $p$-adic $L$-functions. The main conjecture then relates these two sets of objects. Furthermore, we show that the integral Beilinson–Flach elements form a locally restricted Euler system, which in turn allow us to deduce (under certain technical assumptions) one inclusion in each one of the four main conjectures we formulate here (which may be turned into equalities in favorable circumstances).

The Propagation of Shock Waves in Incompressible Fluids: The Case of Freshwater

2014 ◽  
Vol 132 (1) ◽  
pp. 427-437 ◽  
Author(s):  
Andrea Mentrelli ◽  
Tommaso Ruggeri
Keyword(s):  
Shock Waves ◽  
Incompressible Fluids

scholarly journals Uniqueness of Dissipative Solutions to the Complete Euler System

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana
Keyword(s):  
Euler System ◽  
Dissipative Solutions

Adaptive interface thickness based mobility - Phase-field method for incompressible fluids

2021 ◽  
pp. 103687
Author(s):  
Deewakar Sharma ◽  
Mathieu Coquerelle ◽  
Arnaud Erriguible ◽  
Sakir Amiroudine
Keyword(s):  
Phase Field ◽  
Field Method ◽  
Incompressible Fluids ◽  
Phase Field Method ◽  
Interface Thickness ◽  
Adaptive Interface

scholarly journals On the Bloch–Kato conjecture for Hilbert modular forms

2021 ◽  
Author(s):  
Matteo Tamiozzo
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Euler System ◽  
Central Point ◽  
Shimura Curves ◽  
Hilbert Modular Forms ◽  
Reciprocity Laws ◽  
Hilbert Modular ◽  
Special Points

AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

scholarly journals A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions

2021 ◽  
pp. 100038
Author(s):  
R. Chabiniok ◽  
J. Hron ◽  
A. Jarolımová ◽  
J. Málek ◽  
K.R. Rajagopal ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Benchmark Problem ◽  
Slip Boundary Conditions ◽  
Slip Boundary

scholarly journals Odd viscosity in two-dimensional incompressible fluids

2017 ◽  
Vol 2 (9) ◽  
Author(s):  
Sriram Ganeshan ◽  
Alexander G. Abanov
Keyword(s):  
Incompressible Fluids ◽  
Two Dimensional
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