A reaction network approach to the theory of acoustic wave turbulence

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Minh-Binh Tran¹  Craciun, Gheorghe^2,3  Smith, Leslie M.^2,4  Boldyrev, Stanislav⁵ 

[1] Southern Methodist Univ, Dept Math, Dallas, TX 75205 USA

[2] Univ Wisconsin Madison, Dept Math, Madison, WI USA

[3] Univ Wisconsin Madison, Dept Biomol Chem, Madison, WI USA

[4] Univ Wisconsin Madison, Dept Engn Phys, Madison, WI USA

[5] Univ Wisconsin Madison, Dept Phys, Madison, WI USA

关键词: Weak turbulence;    Rate of convergence to equilibrium;    Global attractor conjecture;    Biochemical networks;    Acoustic waves;   

DOI  :  10.1016/j.jde.2020.03.034

来源: Elsevier

【 摘 要 】

We propose a new approach to study the long time dynamics of the wave kinetic equation in the statistical description of acoustic turbulence. The approach is based on rewriting the discrete version of the wave kinetic equation in the form of a chemical reaction network, then employing techniques used to study the Global Attractor Conjecture to investigate the long time dynamics of the newly obtained chemical system. We show that the solution of the chemical system converges to an equilibrium exponentially in time. In addition, a resonance broadening modification of the acoustic wave kinetic equation is also studied with the same technique. For the near-resonance equation, if the resonance broadening frequency is larger than a threshold, the solution of the system goes to infinity as time evolves. Published by Elsevier Inc.

【 授权许可】

Free