On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem

Beirão da Veiga, Hugo. "On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem." Journal of the European Mathematical Society 011.1 (2009): 127-167. <http://eudml.org/doc/277431>.

@article{BeirãodaVeiga2009,
abstract = {We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case $p\ge 2$. Actually, we are interested in proving regularity results in $L^q(\Omega )$ spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced in [3] and [4] for the flat-boundary case, to the case of curvilinear boundaries.},
author = {Beirão da Veiga, Hugo},
journal = {Journal of the European Mathematical Society},
language = {eng},
number = {1},
pages = {127-167},
publisher = {European Mathematical Society Publishing House},
title = {On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem},
url = {http://eudml.org/doc/277431},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Beirão da Veiga, Hugo
TI - On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 1
SP - 127
EP - 167
AB - We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case $p\ge 2$. Actually, we are interested in proving regularity results in $L^q(\Omega )$ spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced in [3] and [4] for the flat-boundary case, to the case of curvilinear boundaries.
LA - eng
UR - http://eudml.org/doc/277431
ER -