L(2)-DECAY RATES FOR WEAK SOLUTIONS OF A PERTURBED NAVIER-STOKES SYSTEM IN R(3)

[摘要] We study global weak solutions u (with generalized energy inequality) of the Cauchy problem for the Navier-Stokes-type system u(t) - DELTAu + v(0). delu + u . delv(0) + u . delu + delpi = 0, div u = 0. Here v(0) is a bounded smooth solenoidal vector field in R3 with v(0) --> v(infinity) as Absolute value of x --> infinity, v(infininty) is-an-element-of R3 is a constant vector. We assume v(0) -v(infinity) is-an-element-of L(p)(R3) for some p is-an-element-of [2, 3) and that the energetic Reynolds number of v(0) is small. In this case we derive explicit decay rates for the kinetic energy of u. (C) 1994 Academic Press, Inc.

[发布日期] 1994-07-15