A remark on the transport equation with b ∈ BV and $div_{x} b ∈ BMO$

Paweł Subko

A remark on the transport equation with b ∈ BV and

d i v_{x} b \in B M O

Paweł Subko

Colloquium Mathematicae, Tome 135 (2014), p. 113-125 / Harvested from The Polish Digital Mathematics Library

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Résumé

We investigate the transport equation $\partial_{t} u (t, x) + b (t, x) \cdot D_{x} u (t, x) = 0$ . Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $d i v_{x} b \in B M O$ . To obtain our result we use a procedure similar to DiPerna and Lions’s one developed for Sobolev vector fields. We apply renormalization theory for BV vector fields and logarithmic type inequalities to obtain energy estimates.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:284145

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     title = {A remark on the transport equation with b [?] BV and $div\_{x} b [?] BMO$
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Paweł Subko. A remark on the transport equation with b ∈ BV and $div_{x} b ∈ BMO$
            . Colloquium Mathematicae, Tome 135 (2014) pp. 113-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-9/