Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity

Abstract EN

We consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity u∞ at infinity.

For u∞=0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in Lp spaces for 1

For the spatial direction, we recently obtained some results.

For u∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability in L2 space.

Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability in Lp spaces for p≥3.

Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense.

In this paper, we improve Bae and Roh's result in the spaces Lp for p>1 and obtain Lr-Lp stability as Kozono and Ogawa and Borchers and Miyakawa obtained for u∞=0.