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arXiv · 1806.04006

An $L^{p}$--approach to the well-posedness of transport equations associated to a regular field

Luisa Arlotti·Bertrand Lods
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Abstract

We investigate transport equations associated to a Lipschitz field on some subspace of $\mathbb{R}^N$ endowedwith a general measure $\mu$ in $L^{p}$-spaces $1 < p <\infty$, extending the results obtained in two previous contributions of the author in the $L^{1}$-context. We notably prove the well-posedness of boundary-value transport problems with a large variety of boundary conditions. New explicit formula for the transport semigroup are in particular given.

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Luisa Arlotti, Bertrand Lods. 2018-06-11. An $L^{p}$--approach to the well-posedness of transport equations associated to a regular field. https://arxiv.org/abs/1806.04006

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