On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients

Maxime Hauray

doi:10.1016/s0294-1449(02)00015-x

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arXiv · 1310.0974

On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients

Maxime Hauray

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Abstract

We consider two-dimensional autonomous divergence free vector-fields in $\Lde_{loc}$. Under a condition on direction of the flow and on the set of critical points, we prove the existence and uniqueness of a stable a.e. flow and of renormalized solutions of the associated transport equation.

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Maxime Hauray. 2013-10-03. On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients. https://doi.org/10.1016/s0294-1449(02)00015-x

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