en
203-247
We consider the Navier–Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting velocity field by space–time-dependent noise that is smooth in space and rough in time. We study the system within the framework of rough path theory and, in particular, the recently developed theory of unbounded rough drivers. We introduce an intrinsic notion of a weak solution of the Navier–Stokes system, establish suitable a priori estimates and prove existence. In two dimensions, we prove that the solution is unique and stable with respect to the driving noise.
https://link.springer.com/10.1007%2Fs00028-018-0473-z
2019-04-11T10:39
2019-03-01
On the Navier–Stokes equation perturbed by rough transport noise
2019-03
articles
research_article
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https://scigraph.springernature.com/explorer/license/
11177c41d4a5cb0ffc235b237f2448818ae43fb14c2b3d1048835c9e76981729
readcube_id
Journal of Evolution Equations
1424-3199
1424-3202
Nilssen
Torstein
Hofmanová
Martina
doi
10.1007/s00028-018-0473-z
19
University of Oslo
Institute of Mathematics, Technical University of Berlin, Berlin, Germany
Department of Mathematics, University of Oslo, Oslo, Norway
Mathematical Sciences
Leahy
James-Michael
pub.1107105539
dimensions_id
Department of Mathematics, University of Southern California, Los Angeles, USA
University of Southern California
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany
Bielefeld University
Institute of Mathematics, Technical University of Berlin, Berlin, Germany
1
Pure Mathematics
Springer Nature - SN SciGraph project