TY - JOUR
T1 - Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions
AU - Berselli , Luigi C.
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 479
EP - 491
PY - 2018
DA - 2018/04
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12526.html
KW - Navier-Stokes equations, Euler scheme, local energy inequality, slip boundary conditions.
AB - <p style="text-align: justify;">We consider the initial boundary value problem for the three dimensional Navier-Stokes
equations with Navier-type slip boundary conditions. After having properly formulated
the problem, we prove that weak solutions constructed by approximating the time-derivative by
backward finite differences (with Euler schemes) are suitable. The main novelty is the proof
of the local energy inequality in the case of a weak solution constructed by time discretization.
Moreover, the problem is analyzed with boundary conditions which are of particular interest in
view of applications to turbulent flows.</p>