LOCAL EXISTENCE THEOREMS WITH UNBOUNDED SET OF INPUT DATA AND UNBOUNDEDNESS OF STABLE INVARIANT MANIFOLDS FOR 3D NAVIER-STOKES EQUATIONS

摘要

Local existence theorem of smooth solution v(t, ·),t∈R_+ for 3D Navier-Stokes equations is proved, when initial data belongs to a certain unbounded ellipsoid of suitable function space. Unboundedness of stable invariant manifolds for 3D Navier-Stokes equations is proved as well.