ISSN:
1573-8698
Keywords:
93B05
;
93C20
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
abstract In a bounded three-dimensional domain Ω a solenoidal initial vector fieldv 0(x)∈H 3 (Ω) is given. We construct a vector fieldz(t, x) defined on the lateral surface [0,T]×ϖΩ of the cylinder [0,T]×Ω which possesses the following property: the solutionv(t, x) of the boundary value problem for the Navier-Stokes equation with the initial valuev 0(x) and the boundary Dirichlet conditionz(t, x) satisfies the relationv(T, x)≡0 at the instantT. Moreover, $$\parallel v(t, \cdot )\parallel _{H^3 (\Omega )} \leqslant c\exp \left( { - k/(T - t)^2 } \right) as t \to T$$ , wherec〉0,k〉0 are certain constants.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02269373
Permalink