Zakharov system on R^2: Difference between revisions
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Revision as of 06:35, 27 July 2006
Zakharov systems do not have a true scale invariance, but the critical regularity is (s0,s1) = (-1/2,-1).
LWP for (s0,s1) = (1/2,0) [GiTsVl1997]
For (s0,s1) = (1,0) this was proven in [BoCo1996], [Co1997].
GWP for small (1,0) data [BoCo1996]; the smallness is needed to control the nonquadratic portion of the energy.
As long as the H1 norm remains bounded (which is automatic for small data), the higher H^s norms of u grow by at most |t|(s-1)+ [CoSt-p]
Explicit blowup solutions have been constructed with a blowup rate of t-1 in H1 norm [GgMe1994], [GgMe1994b]. This is optimal in the sense that no slower blowup rate is possible [Me1996b]
