Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig. "Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle." Banach Center Publications 70.1 (2005): 73-84. <http://eudml.org/doc/282367>.

@article{ReinhardFarwig2005,
abstract = {Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved $L^q$-estimates of second order derivatives uniformly in the angular and translational velocities, ω and k, of the obstacle, whereas the transport terms fails to have $L^q$-estimates independent of ω. In this paper we clarify this unexpected behavior and prove weighted $L^q$-estimates of first order terms independent of ω.},
author = {Reinhard Farwig},
journal = {Banach Center Publications},
keywords = {-estimates; weighted -estimates},
language = {eng},
number = {1},
pages = {73-84},
title = {Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle},
url = {http://eudml.org/doc/282367},
volume = {70},
year = {2005},
}

TY - JOUR
AU - Reinhard Farwig
TI - Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle
JO - Banach Center Publications
PY - 2005
VL - 70
IS - 1
SP - 73
EP - 84
AB - Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved $L^q$-estimates of second order derivatives uniformly in the angular and translational velocities, ω and k, of the obstacle, whereas the transport terms fails to have $L^q$-estimates independent of ω. In this paper we clarify this unexpected behavior and prove weighted $L^q$-estimates of first order terms independent of ω.
LA - eng
KW - -estimates; weighted -estimates
UR - http://eudml.org/doc/282367
ER -