On the Kinetic Equation in Zakharov's Wave Turbulence Theory for Capillary Waves

DOI10.1137/17M1125042zbMath1459.82152arXiv1702.03892WikidataQ130014931 ScholiaQ130014931MaRDI QIDQ4634706

Minh-Binh Tran, Toan T. Nguyen

Publication date: 11 April 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03892

zbMATH Keywords

capillary wavesweak turbulence theoryfluids mechanicsquantum Boltzmannwater waves systemkinetic wave equationsZakharov's wave turbulence theory

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Continuation and prolongation of solutions to PDEs (35B60) Strong solutions to PDEs (35D35) Boltzmann equations (35Q20)

Related Items (8)

A reaction network approach to the theory of acoustic wave turbulence ⋮ Optimal local well-posedness theory for the kinetic wave equation ⋮ On the energy cascade of 3-wave kinetic equations: beyond Kolmogorov-Zakharov solutions ⋮ A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations ⋮ On the wave turbulence theory for stratified flows in the ocean ⋮ On coupling kinetic and Schrödinger equations ⋮ Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons ⋮ Quantum hydrodynamic approximations to the finite temperature trapped Bose gases

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