A remark on the transport equation with b ∈ BV and $di{v}_{x}b\in BMO$

Paweł Subko. "A remark on the transport equation with b ∈ BV and $div_{x} b ∈ BMO$." Colloquium Mathematicae 135.1 (2014): 113-125. <http://eudml.org/doc/284145>.

@article{PawełSubko2014,
abstract = {We investigate the transport equation $∂_\{t\}u(t,x) + b(t,x)·D_\{x\}u(t,x) = 0$. Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $div_x b ∈ BMO$. 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.},
author = {Paweł Subko},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {113-125},
title = {A remark on the transport equation with b ∈ BV and $div_\{x\} b ∈ BMO$},
url = {http://eudml.org/doc/284145},
volume = {135},
year = {2014},
}

TY - JOUR
AU - Paweł Subko
TI - A remark on the transport equation with b ∈ BV and $div_{x} b ∈ BMO$
JO - Colloquium Mathematicae
PY - 2014
VL - 135
IS - 1
SP - 113
EP - 125
AB - We investigate the transport equation $∂_{t}u(t,x) + b(t,x)·D_{x}u(t,x) = 0$. Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $div_x b ∈ BMO$. 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.
LA - eng
UR - http://eudml.org/doc/284145
ER -