Zakharov system on R^3

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The theory for the Zakharov system on R^3 is as follows.

  • The Zakharov system does not have a true scale invariance, but the critical regularity is (s0,s1) = (0,-1/2).
  • Local well-posedness for (1/2,0) (GiTsVl1997)
    • For (s0,s1) = (1,0) this was proven in BoCo1996.
  • GWP for small smooth data is in OzTs1994.