Geodesic
A remark on the transport equation with $b\in {\rm BV}$ and ${\rm div}_{x}\, b\in {\rm BMO}$
Paweł Subko1
1 Institute of Applied Mathematics and Mechanics University of Warsaw 02-097 Warszawa, Poland
Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 113-125.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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: $b\in {\rm BV}$, ${\rm div}_x\, b\in {\rm BMO}$. 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.
DOI : 10.4064/cm135-1-9
Keywords: investigate transport equation partial x cdot t result improves classical criteria uniqueness weak solutions irregular coefficients div bmo obtain result procedure similar diperna lionss developed sobolev vector fields apply renormalization theory vector fields logarithmic type inequalities obtain energy estimates

Paweł Subko 1

1 Institute of Applied Mathematics and Mechanics University of Warsaw 02-097 Warszawa, Poland 
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Paweł Subko. A remark on the transport equation with $b\in {\rm BV}$
 and ${\rm div}_{x}\, b\in {\rm BMO}$. Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 113-125. doi : 10.4064/cm135-1-9. http://geodesic.mathdoc.fr/articles/10.4064/cm135-1-9/

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