The law of the iterated logarithm for the solution of the Burgers equation with random initial data
type: Item
instance of: scholarly article
title: The law of the iterated logarithm for the solution of the Burgers equation with random initial data
zbMATH Open document ID: 0944.60069
DOI: 10.1007/BF02313027
author: Yuri Bakhtin
published in: Mathematical Notes
publication date: 2000-09-13T00:00:00Z
review text: It is proved that for the solution \(v(t,x)\) of \(\frac{\partial v}{\partial t} + (v,\nabla)v=\kappa\nabla v\), \(v(0,x)=-2\kappa\nabla\xi(x)\), \((t,x)\in \mathbb{R}^1_+\times \mathbb{R}^1\) with \(\xi\) a zero-range shot noise the relation \(\varlimsup_{t\rightarrow\infty} \frac{|v(t,x)|}{ct^{3/4}(\ln\ln t)^{1/2}} =1\) (almost everywhere) holds.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1407593
zbMATH Keywords: Burgers equation
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: shot noise
reviewed by: Wilfried Grecksch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1407593