Enhanced Dissipation for Two-Dimensional Hamiltonian Flows

被引:0
作者
Brue, Elia [1 ]
Zelati, Michele Coti [2 ]
Marconi, Elio [3 ]
机构
[1] Bocconi Univ, Dept Decis Sci, Via Sarfatti 25, I-20136 Milan, MI, Italy
[2] Imperial Coll London, Dept Math, London SW7 2AZ, England
[3] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, PD, Italy
基金
欧盟地平线“2020”;
关键词
35Q35; 35Q49; 76F25; CELLULAR FLOWS; DIFFUSION; TRANSPORT; EQUATIONS;
D O I
10.1007/s00205-024-02034-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let H is an element of C1 boolean AND W2,pbe an autonomous, non-constant Hamiltonian on a compact2-dimensional manifold, generating an incompressible velocity fieldb= del H-perpendicular to.We give sharp upper bounds on the enhanced dissipation rate ofbin terms of theproperties of the periodT(h)of the closed orbit{H=h}. Specifically, if 0<nu(-1)is the diffusion coefficient, the enhanced dissipation rate can be at mostO(nu(1/3))ingeneral, the bound improves whenHhas isolated, non-degenerate elliptic points.Our result provides the better boundO(nu(1/2))for the standard cellular flow given by Hc(x)=sinx(1) sinx(2), for which we can also prove a new upper bound on its mixingrate and a lower bound on its enhanced dissipation rate. The proofs are based onthe use of action-angle coordinates and on the existence of a good invariant domain for the regular Lagrangian flow generated by b.
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页数:37
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