Zakharov system on R: Difference between revisions
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Zakharov on R and T | * Zakharov systems do not have a true scale invariance, but the critical regularity is (s0,s1) = (-1,-3/2). | ||
* LWP on R for (0,-1/2), or more generally whenever -1/2 < s0 - s1 £ 1 and 2s0³ s1 + 1/2 ³ 0 [GiTsVl1997] | |||
** On T (with irrational period) the same result holds but one must place the additional restriction 0 £ s0 - s1 [Tk-p3]. | |||
** For general period, a slightly weaker version of this (assuming weighted pointwise bounds on Fourier co-efficients, and establishing an invariant Gibbs measure), is in [Bo1994] | |||
* GWP on R for (9/10+,0) [Pe-p]. | |||
* In the energy class (1,0) this was shown in [GiTsVl1997]. | |||
[[Category:Equations]] | |||
Revision as of 05:58, 27 July 2006
- Zakharov systems do not have a true scale invariance, but the critical regularity is (s0,s1) = (-1,-3/2).
- LWP on R for (0,-1/2), or more generally whenever -1/2 < s0 - s1 £ 1 and 2s0³ s1 + 1/2 ³ 0 [GiTsVl1997]
- On T (with irrational period) the same result holds but one must place the additional restriction 0 £ s0 - s1 [Tk-p3].
- For general period, a slightly weaker version of this (assuming weighted pointwise bounds on Fourier co-efficients, and establishing an invariant Gibbs measure), is in [Bo1994]
- GWP on R for (9/10+,0) [Pe-p].
- In the energy class (1,0) this was shown in [GiTsVl1997].