TY - JOUR
T1 - Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system
AU - Germain, Pierre
PY - 2008/1
Y1 - 2008/1
N2 - This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes system in dimension d > 3. We use new a priori estimates, which enable us to deal with low-regularity data and vanishing density. In particular, we prove new well-posedness results which improve the results of Danchin [6] by considering a less regular initial density, without a lower bound. Also, we obtain the first uniqueness criterion for weak solutions which is at the scaling of the equation.
AB - This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes system in dimension d > 3. We use new a priori estimates, which enable us to deal with low-regularity data and vanishing density. In particular, we prove new well-posedness results which improve the results of Danchin [6] by considering a less regular initial density, without a lower bound. Also, we obtain the first uniqueness criterion for weak solutions which is at the scaling of the equation.
UR - http://www.scopus.com/inward/record.url?scp=58449101526&partnerID=8YFLogxK
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U2 - 10.1007/s11854-008-0034-4
DO - 10.1007/s11854-008-0034-4
M3 - Article
AN - SCOPUS:58449101526
SN - 0021-7670
VL - 105
SP - 169
EP - 196
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -