_t u+u __ u- __u = -_p R_R3
div u= 0
Continuation Theorem
(SERRIN)
MAIN OPEN PROBLEMS
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 velocity u remains uniformly bounded; in fact as long as
Local in time existence
3 Global Regularity for Navier-Stokes
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