Closure and complete integrability in Burgers turbulence

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Overview

Title
Closure and complete integrability in Burgers turbulence
Contributors
Srinivasan, Ravi (creator)
Menon, Govind (director)
Menon, Govind (reader)
Dafermos, Constantine (reader)
Rozovsky, Boris (reader)
Brown University. Applied Mathematics (sponsor)
Doi
10.7301/Z05B00RX
Copyright Date
2009
Abstract
Burgers turbulence (1-D inviscid Burgers equation with random initial data) is a fundamental non-equilibrium model of stochastic coalescence. In this work we demonstrate that at the level of the 2-point correlation function, the entropy solution to Burgers equation yields a closed, completely integrable system. We show that the statistical evolution is given by a Lax pair. Finally, we demonstrate that this equation has an equivalent kinetic description with a rich family of self-similar solutions, and in particular admits an explicit solution derived by Groeneboom in nonparametric statistics. Finally, the closure property and complete integrability are shown to hold in the general case of 1-D scalar conservation laws with strictly convex flux.
Keywords
Burgers turbulence
statistical closures
complete integrability
stochastic coalescence
kinetic theory
coagulation equations
Notes
Thesis (Ph.D.) -- Brown University (2009)
Extent
viii, 77 p.

Citation

Srinivasan, Ravi, "Closure and complete integrability in Burgers turbulence" (2009). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.7301/Z05B00RX

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