PPT Slide

WELL POSED

• Hs(loc)-initial data ? local in time, unique Hs(loc)-solutions.
  
  The solutions depend continuously on the data:
• strong - analytically
• weak - nonanalytically

WELL POSEDNESS, CRITICAL EXPONENT

CRITICAL EXPONENT s = sc

Hs is invariant under the nonlinear scaling of the equations.

CONJECTURE:

Well posed for
Hs(loc)- data for any s > sc.

Weakly globally well posed for
s = sc and small initial data.

The genaral weak solutions corresponding to s < sc are meaningless. “Weak solutions are Ghosts”

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