# American Institute of Mathematical Sciences

June  2010, 3(2): 269-289. doi: 10.3934/dcdss.2010.3.269

## Local existence theorems with unbounded set of input data and unboundedness of stable invariant manifolds for 3D Navier-Stokes equations

 1 Department of Mechanics & Mathematics, Moscow State University, Moscow 119991, Russian Federation

Received  March 2009 Revised  September 2009 Published  April 2010

Local existence theorem of smooth solution $v(t,\cdot), t\in \R_+$ 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.
Citation: Andrei Fursikov. Local existence theorems with unbounded set of input data and unboundedness of stable invariant manifolds for 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 269-289. doi: 10.3934/dcdss.2010.3.269
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