Symplectic embeddings from R2n into some manifolds

2000 ◽  
Vol 130 (1) ◽  
pp. 53-61 ◽  
Author(s):  
M.-Y. Jiang
Keyword(s):  
Symplectic Manifold ◽  
Symplectic Form ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Symplectic Capacity ◽  
Elementary Methods

We show by elementary methods that there are symplectic embeddings from standard (R2n, ω0) into (Σ x R2n−2, ω ⊕ ω0) and (T2n−2k x R2k, ω ⊕ ω0), where (Σ, ω) is a closed two-dimensional symplectic manifold, and (T2n−2k, ω) is the torus with a constant symplectic form ω. Some estimates of Gromov's symplectic capacity are given for bounded domains in these manifolds.

Hofer–Zehnder symplectic capacity for two-dimensional manifolds

1993 ◽  
Vol 123 (5) ◽  
pp. 945-950 ◽  
Author(s):  
Mei-Yue Jiang
Keyword(s):  
Symplectic Form ◽  
Cotangent Bundle ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Symplectic Capacity

SynopsisIn this paper, we show that the Hofer-Zehnder symplectic capacity of a two-dimensional manifold is same as the area of the manifold. Using this fact, we also get a result on the symplectic capacity of the cotangent bundle of the torus with its canonical symplectic form.

Weak solutions for generalized stationary Oldroyd-B fluid with a diffusive stress

2016 ◽  
Vol 23 (4) ◽  
pp. 469-475
Author(s):  
Hafedh Bousbih ◽  
Mohamed Majdoub
Keyword(s):  
Stress Tensor ◽  
Weak Solutions ◽  
Fluid Model ◽  
Three Dimensional ◽  
Shear Thickening ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Existence Of Weak Solutions ◽  
Elastic Part ◽  
Viscosity Function

AbstractThis paper focuses on the analysis of the stationary case of incompressible viscoelastic generalized Oldroyd-B fluids derived in [2] by Bejaoui and Majdoub. The studied model is different from the classical Oldroyd-B fluid model in having a viscosity function which is shear-rate depending, and a diffusive stress added to the equation of the elastic part of the stress tensor. Under some conditions on the viscosity stress tensor and for a large class of models, we prove the existence of weak solutions in both two-dimensional and three-dimensional bounded domains for shear-thickening flows.

scholarly journals Geometric prequantization on the path space of a prequantized manifold

2015 ◽  
Vol 12 (03) ◽  
pp. 1550030
Author(s):  
Indranil Biswas ◽  
Saikat Chatterjee ◽  
Rukmini Dey
Keyword(s):  
Symplectic Manifold ◽  
Symplectic Form ◽  
Symplectic Structure ◽  
Gordon Equation ◽  
Solution Space ◽  
Path Space ◽  
Klein Gordon ◽  
Class Of Functions ◽  
Compact Symplectic Manifold ◽  
Klein Gordon Equation

Given a compact symplectic manifold M, with integral symplectic form, we prequantize a certain class of functions on the path space for M. The functions in question are induced by functions on M. We apply our construction to study the symplectic structure on the solution space of Klein–Gordon equation.

scholarly journals Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Hong Yin
Keyword(s):  
Incompressible Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Finite Dimensional

The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations. Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.

scholarly journals Symmetry Results for Nonvariational Quasi-Linear Elliptic Systems

2010 ◽  
Vol 10 (4) ◽  
Author(s):  
Luigi Montoro ◽  
Berardino Sciunzi ◽  
Marco Squassina
Keyword(s):  
Half Space ◽  
Comparison Principle ◽  
Axial Symmetry ◽  
Elliptic Systems ◽  
Radial Symmetry ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Regular Solutions ◽  
Variational Form ◽  
Weak Comparison Principle

AbstractBy virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in non-variational form. Moreover, in the two dimensional case, we study the system when set in a half-space.

scholarly journals Global weak solutions to the stochastic Ericksen–Leslie system in dimension two

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hengrong Du ◽  
Changyou Wang
Keyword(s):  
System Modeling ◽  
Energy Estimates ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Global Weak Solutions ◽  
Tensor Fields ◽  
Ginzburg Landau ◽  
Wiener Type ◽  
Leslie System ◽  
Martingale Solutions

<p style='text-indent:20px;'>We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen–Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg–Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and then the Skorokhod compactness theorem, which is built upon uniform energy estimates.</p>

Isotropic model of fractional transport in two-dimensional bounded domains

2013 ◽  
Vol 87 (5) ◽  
Author(s):  
A. Kullberg ◽  
D. del-Castillo-Negrete ◽  
G. J. Morales ◽  
J. E. Maggs
Keyword(s):  
Bounded Domains ◽  
Two Dimensional ◽  
Isotropic Model ◽  
Fractional Transport

RENORMALIZATION PROPERTIES OF TWO-DIMENSIONAL HOMOGENEOUS SYMPLECTIC σ-MODELS

1992 ◽  
Vol 07 (24) ◽  
pp. 2229-2233 ◽  
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Finite Number ◽  
Symplectic Manifold ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Dimensional Matrix ◽  
Finite Dimensional ◽  
Renormalization Constants

The structure of renormalization of the two-dimensional σ-model, built on an arbitrary homogeneous symplectic manifold, is found within a convenient parametrization of the fields. Solution of the Ward-Takahashi (WT) identities determines the renormalized action up to a finite number of renormalization constants. All the infinities can be absorbed in a coupling constants renormalization and in a renormalization of an auxiliary constant finite-dimensional matrix.

Sign in / Sign up

Export Citation Format

Share Document