Sharp Rellich-Leray inequality for axisymmetric divergence-free vector fields

2019 ◽  
Vol 58 (4) ◽  
Author(s):  
Naoki Hamamoto
Keyword(s):  
Vector Fields ◽  
Divergence Free Vector ◽  
Divergence Free

scholarly journals On volume-preserving vector fields and finite-type invariants of knots

2014 ◽  
Vol 36 (3) ◽  
pp. 832-859 ◽  
Author(s):  
R. KOMENDARCZYK ◽  
I. VOLIĆ
Keyword(s):  
Finite Type ◽  
Configuration Space ◽  
Vector Fields ◽  
Finite Type Invariants ◽  
Linking Number ◽  
Divergence Free Vector ◽  
Divergence Free ◽  
Volume Preserving ◽  
Configuration Space Integrals

We consider the general non-vanishing, divergence-free vector fields defined on a domain in$3$-space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.

scholarly journals Vector fields satisfying the barycenter property

2018 ◽  
Vol 16 (1) ◽  
pp. 429-436 ◽  
Author(s):  
Manseob Lee
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Axiom A ◽  
Divergence Free Vector ◽  
Divergence Free ◽  
Volume Preserving

AbstractWe show that if a vector fieldXhas theC1robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a genericC1-vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].

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