On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients
arXiv:1310.0974 · doi:10.1016/S0294-1449(02)00015-X
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.
17 pages