On Two-dimensional Hamiltonian Transport Equations with L^p_(loc) coefficients
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flowtransporttwo-dimensionalassociatedautonomouscoefficientsconditionconsider
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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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