Leading terms of velocity and its gradient of the stationary rotational viscous incompressible flows with nonzero velocity at infinity

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a previous paper, we prove a representation formula for weak solutions of the system. Here the representation formula is used to get an asymptotic expansion of respectively velocity and its gradient, and to establish pointwise decay estimates of remainder terms. Our results are based on a fundamental solution proposed by Guenther and Thomann J. Math. Fluid Mech., 8 (2006), 77-98. We thus present a different approach to this result, besides the one, given by Kyed J. Math. Soc. Japan, 66 (2014), 1-16.

[1]  P. Deuring,et al.  Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions , 2014 .

[2]  P. Deuring,et al.  Pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity , 2013 .

[3]  R. Farwig,et al.  The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body , 2013 .

[4]  M. Kyed.  On a mapping property of the Oseen operator with rotation , 2013 .

[5]  G. Galdi,et al.  A simple proof of L q -estimates for the steady-state Oseen and Stokes equations in a rotating frame. Part I: Strong solutions , 2012 .

[6]  R. Farwig,et al.  Asymptotic structure of a Leray solution to the Navier–Stokes flow around a rotating body , 2011 .

[7]  R. Farwig,et al.  Leading term at infinity of steady Navier‐Stokes flow around a rotating obstacle , 2011 .

[8]  P. Deuring,et al.  A linearized system describing stationary incompressible viscous flow around rotating and translating bodies: Improved decay estimates of the velocity and its gradient , 2011 .

[9]  R. Farwig,et al.  Asymptotic profile of steady Stokes flow around a rotating obstacle , 2011 .

[10]  Giovanni P. Galdi,et al.  An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems , 2011 .

[11]  G. Galdi,et al.  Steady-State Navier–Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable , 2011 .

[12]  Paul Deuring,et al.  On Pointwise Decay of Linearized Stationary Incompressible Viscous Flow around Rotating and Translating Bodies , 2011, SIAM J. Math. Anal..

[13]  C. Amrouche,et al.  Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data , 2011 .

[14]  R. Farwig,et al.  Asymptotic profiles of steady Stokes and Navier–Stokes flows around a rotating obstacle , 2009 .

[15]  Y. Shibata,et al.  Lp-Lq Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle , 2009 .

[16]  R. Farwig,et al.  A weighted Lq-approach to Stokes flow around a rotating body , 2008 .

[17]  R. Farwig,et al.  A weighted Lq‐approach to Oseen flow around a rotating body , 2008 .

[18]  R. Farwig,et al.  On the spectrum of a Stokes-type operator arising from flow around a rotating body , 2007 .

[19]  Matthias Geissert,et al.  L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle , 2006 .

[20]  Toshiaki Hishida,et al.  $L^q$ estimates of weak solutions to the stationary Stokes equations around a rotating body , 2006 .

[21]  E. Thomann,et al.  The Fundamental Solution of the Linearized Navier–Stokes Equations for Spinning Bodies in Three Spatial Dimensions – Time Dependent Case , 2006 .

[22]  Š. Nečasová.  Asymptotic properties of the steady fall of a body in viscous fluids , 2004 .

[23]  P. Deuring,et al.  Exterior stationary Navier‐Stokes flows in 3D with non‐zero velocity at infinity: approximation by flows in bounded domains , 2004 .

[24]  R. Farwig,et al.  Lq-theory of a singular "winding'' integral operator arising from fluid dynamics , 2004 .

[25]  Giovanni P. Galdi,et al.  Steady Flow of a Navier-Stokes Fluid Around a Rotating Obstacle , 2003 .

[26]  Giovanni P. Galdi,et al.  Chapter 7 – On the Motion of a Rigid Body in a Viscous Liquid: A Mathematical Analysis with Applications , 2002 .

[27]  Toshiaki Hishida,et al.  An Existence Theorem¶for the Navier-Stokes Flow¶in the Exterior of a Rotating Obstacle , 1999 .

[28]  R. Farwig.  The stationary exterior 3 D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces , 1992 .

[29]  M. Kyed.  On the asymptotic structure of a Navier-Stokes flow past a rotating body , 2014 .

[30]  P. Deuring,et al.  Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity , 2012 .

[31]  G. Galdi,et al.  Asymptotic Behavior of a Leray Solution around a Rotating Obstacle , 2011 .

[32]  Š. Nečasová,et al.  Anisotropic $L^{2}$-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body , 2010 .

[33]  C. Amrouche,et al.  On the stationary Oseen equations in R 3 , 2008 .

[34]  R. Farwig,et al.  Stationary Navier-Stokes Flow Around a Rotating Obstacle , 2007 .

[35]  R. Farwig.  Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle , 2005 .

[36]  P. Penel,et al.  New regularity results for a generic model equation in exterior 3D domains , 2005 .

[37]  P. Penel,et al.  Variational Properties of a Generic Model Equation in Exterior 3D Domains , 2004 .

[38]  A. Novotný,et al.  Estimates of Oseen kernels in weighted L^p spaces , 2001 .

[39]  T. Hishida.  THE STOKES OPERATOR WITH ROTATION EFFECT IN EXTERIOR DOMAINS , 1999 .

[40]  G. Galdi.  An Introduction to the Mathematical Theory of the Navier-Stokes Equations : Volume I: Linearised Steady Problems , 1994 .