scholarly journals A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space

2013 ◽  
Vol 141 (8) ◽  
pp. 2793-2798 ◽  
Author(s):  
Luc Molinet
Keyword(s):  
Burgers Equation ◽  
Energy Space ◽  
Inviscid Limit

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

scholarly journals Uniform well-posedness and inviscid limit for the Benjamin–Ono–Burgers equation

2011 ◽  
Vol 228 (2) ◽  
pp. 647-677 ◽  
Author(s):  
Zihua Guo ◽  
Lizhong Peng ◽  
Baoxiang Wang ◽  
Yuzhao Wang
Keyword(s):  
Burgers Equation ◽  
Inviscid Limit ◽  
Well Posedness

scholarly journals Stochastic turbulence for Burgers equation driven by cylindrical Lévy process

2021 ◽  
Author(s):  
Shenglan Yuan ◽  
Dirk Blömker ◽  
Jinqiao Duan
Keyword(s):  
Kinematic Viscosity ◽  
Burgers Equation ◽  
Inviscid Limit ◽  
Regularity Of Solutions ◽  
One Dimensional ◽  
Stochastic Dynamical System ◽  
Qualitative And Quantitative ◽  
Stochastic Burgers Equation ◽  
Quantitative Properties ◽  
Turbulent Velocity Field

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [Formula: see text] tends towards zero. The inviscid limit describes the strong stochastic turbulence.

scholarly journals Inviscid limit to the shock waves for the fractal Burgers equation

2020 ◽  
Vol 18 (6) ◽  
pp. 1477-1491
Author(s):  
Sona Akopian ◽  
Moon-Jin Kang ◽  
Alexis Vasseur
Keyword(s):  
Shock Waves ◽  
Burgers Equation ◽  
Inviscid Limit

scholarly journals THE INVISCID LIMIT OF THE MODIFIED BENJAMIN–ONO–BURGERS EQUATION

2010 ◽  
Vol 83 (2) ◽  
pp. 301-320
Author(s):  
HUA ZHANG ◽  
YUQIN KE
Keyword(s):  
Initial Data ◽  
Burgers Equation ◽  
Inviscid Limit ◽  
Dissipative Coefficient ◽  
Well Posed

AbstractWe prove that the modified Benjamin–Ono–Burgers equation is globally well-posed in Hs for s>0. Moreover, we show that the solution of the modified Benjamin–Ono–Burgers equation converges to that of the modified Benjamin–Ono equation in the natural space C([0,T];Hs), s≥1/2, as the dissipative coefficient ϵ goes to zero, provided that the L2 norm of the initial data is sufficiently small.

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