_t u+u __ u= -_p R_R3
div u= 0
Continuation Theorem
(BEALS-KATO-MAJDA)
MAIN OPEN PROBLEMS
2 Break-down for 3D Euler Equations
Initial Data (regular) u(0, x)=u0 ( x )
Known Results
For any smooth initial data there exists
a T>0 and a unique solution in [0,T]_R3.
The solution can be smoothly continued as long as the vorticity _ remains uniformly bounded; in fact as long as
Local in time existence
Vorticity _=__u
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