scholarly journals Backward semi-martingales into Burgers turbulence

2021 ◽  
Vol 62 (6) ◽  
pp. 061506
Author(s):  
Florent Nzissila ◽  
Octave Moutsinga ◽  
Fulgence Eyi Obiang
Keyword(s):  
Burgers Turbulence

Burgers Turbulence and Dynamical Systems

2001 ◽  
pp. 429-443
Author(s):  
Renato Iturriaga ◽  
Konstantin Khanin
Keyword(s):  
Dynamical Systems ◽  
Burgers Turbulence

A practical comparison between the spectral techniques in solving the SDEs

2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed El-Beltagy
Keyword(s):  
Infinite Number ◽  
Random Variables ◽  
Nonlinear Problems ◽  
Hermite Expansion ◽  
Content Type ◽  
Spectral Techniques ◽  
Burgers Turbulence ◽  
Non Gaussian ◽  
Convergence Orders ◽  
Lipschitz Conditions

Purpose The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite expansion (WHE). The details of the two decompositions are outlined. The difficulties arise when using the two techniques are also mentioned along with the convergence orders. The reader can also find a collection of references to understand the two decompositions with their origins. The geometrical Brownian motion is considered as an example for an important process with exact solution for the sake of comparison. The two decompositions are found practical in analysing the SDEs. The WCE is, in general, simpler, while WHE is more efficient as it is the limit of WCE when using infinite number of random variables. The Burgers turbulence is considered as a nonlinear example and WHE is shown to be more efficient in detecting the turbulence. In general, WHE is more efficient especially in case of nonlinear and/or non-Gaussian processes. Design/methodology/approach The paper outlined the technical and literature review of the WCE and WHE techniques. Linear and nonlinear processes are compared to outline the comparison along with the convergence of both techniques. Findings The paper shows that both decompositions are practical in solving the stochastic differential equations. The WCE is found simpler and WHE is the limit when using infinite number of random variables in WCE. The WHE is more efficient especially in case of nonlinear problems. Research limitations/implications Applicable for SDEs with square integrable processes and coefficients satisfying Lipschitz conditions. Originality/value This paper fulfils a comparison required by the researchers in the stochastic analysis area. It also introduces a simple efficient technique to model the flow turbulence in the physical domain.

scholarly journals Burgers' turbulence problem with linear or quadratic external potential

2005 ◽  
Vol 42 (02) ◽  
pp. 550-565 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
N. N. Leonenko
Keyword(s):  
Burgers Equation ◽  
Initial Conditions ◽  
External Potential ◽  
Limit Laws ◽  
Random Initial Conditions ◽  
Burgers Turbulence

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

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