On L 1 - Stability of Stationary Navier - Stokes Flows in
نویسندگان
چکیده
Stability of stationary Navier-Stokes flows in , n ≥ 3, is discussed in the function space L or H (Hardy space). It is shown that a stationary flow w is stable in H (resp. L) if sup |x| · |w(x)| + sup |x|2|∇w(x)| (resp. ‖w‖(n,1) + ‖∇w‖(n/2,1)) is small. Explicit decay rates of the form O(t−β/2), 0 < β ≤ 1, are deduced for perturbations under additional assumptions on w and on initial data. The proofs of the results heavily rely on the theory of Hardy spaces H (0 < p ≤ 1) of Fefferman and Stein.
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