TY - JOUR
T1 - Sobolev regular flows of non-Lipschitz vector fields
AU - Clop, Albert
AU - Jylhä, Heikki
PY - 2019/4/5
Y1 - 2019/4/5
N2 - We show that vector fields with exponentially integrable derivatives admit a well defined flow of homeomorphisms X(t,⋅)∈W1,p(t)loc for some p(t)>1, at least for small times. When the field is certain Riesz potential of a bounded function, the result becomes global in time, due to techniques from Geometric Function Theory. The local result also applies to the flows arising from Yudovich solutions to the planar Euler system with bounded vorticity.
AB - We show that vector fields with exponentially integrable derivatives admit a well defined flow of homeomorphisms X(t,⋅)∈W1,p(t)loc for some p(t)>1, at least for small times. When the field is certain Riesz potential of a bounded function, the result becomes global in time, due to techniques from Geometric Function Theory. The local result also applies to the flows arising from Yudovich solutions to the planar Euler system with bounded vorticity.
UR - http://www.mendeley.com/research/sobolev-regular-flows-nonlipschitz-vector-fields
UR - https://www.scopus.com/pages/publications/85054434975
U2 - 10.1016/j.jde.2018.10.002
DO - 10.1016/j.jde.2018.10.002
M3 - Article
SN - 0022-0396
VL - 266
SP - 4544
EP - 4567
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -