Some remarks on Li-Sinai-type solutions of the Burgers equation

Pauls, W.

doi:10.1088/1751-8113/44/28/285209

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Some remarks on Li-Sinai-type solutions of the Burgers equation

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Pauls, W.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Pauls, W. (2011). Some remarks on Li-Sinai-type solutions of the Burgers equation. Journal of Physics A: Mathematical and Theoretical, 44(28): 285209. doi:10.1088/1751-8113/44/28/285209.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-332A-A

Abstract

For a class of complex-valued initial conditions, we construct solutions for the inviscid Burgers equations of the same type as those recently introduced by Li and Sinai. Obtained by very simple considerations, these solutions correspond to stable distributions with 1 < α ≤ 2. We furthermore show that solutions of non-Gaussian type can be constructed for the viscous Burgers equation.