Calculus of Variations and Geometric Measure Theory
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F. Colombini - G. Crippa - J. Rauch

A note on two dimensional transport with bounded divergence

created by crippa on 23 May 2005
modified on 24 May 2006


Published Paper

Inserted: 23 may 2005
Last Updated: 24 may 2006

Journal: Comm. Partial Differential Equations
Volume: 31
Number: 7
Pages: 1109 - 1115
Year: 2006


\documentclass{article} \begin{document}

We prove uniqueness for two dimensional transport across a noncharacteristic curve, under the hypothesis that the vector field is autonomous, bounded and with bounded divergence. We also obtain uniqueness for the Cauchy problem in $\mathbf{R}_t \times \mathbf{R}^2_x$ under an additional condition on the local direction of the vector field. \end{document}

Keywords: Renormalized solutions, Transport equation


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