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On two-dimensional Hamiltonian transport equations with $$\mathbb L^p_{\text{loc}}$$ coefficients. (English) Zbl 1028.35148
F. Bouchut and L. Desvillettes [Differ. Integral Equ. 14, 1015-1024 (2001; Zbl 1028.35042)] analysed the Hamiltonian transport equation with continuous coefficient. Their consideration based on the fact that the equivalent ordinary differential equation may be solved. Here this method is generalized for less regularity of the coefficients.

##### MSC:
 35R05 PDEs with low regular coefficients and/or low regular data 82C70 Transport processes in time-dependent statistical mechanics 35F10 Initial value problems for linear first-order PDEs
##### Keywords:
existence; uniqueness; Hamiltonian transport equation
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##### References:
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