In this survey we describe some well-posedness results for the linear transport equation that are available in the two-dimensional case. Due to the special structure of the problem, which admits a Hamiltonian function conserved (at least formally) by the flow, the assumptions needed for the uniqueness are dramatically weaker than those needed for general bounded vector fields in R^N.
Divergence-free vector fields in R^2
ALBERTI, GIOVANNI;
2010-01-01
Abstract
In this survey we describe some well-posedness results for the linear transport equation that are available in the two-dimensional case. Due to the special structure of the problem, which admits a Hamiltonian function conserved (at least formally) by the flow, the assumptions needed for the uniqueness are dramatically weaker than those needed for general bounded vector fields in R^N.File in questo prodotto:
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