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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 -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 -estimates independent of ω. In this paper we clarify this unexpected behavior and prove weighted -estimates of first order terms independent of ω.
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 -