论文标题
Zakharov系统的随机最终状态问题在维度三
Randomized final-state problem for the Zakharov system in dimension three
论文作者
论文摘要
我们考虑了三个空间维度在能量空间中Zakharov系统的最终状态问题。对于$（u_+，v_+）\在h^1 \ times l^2 $中，没有任何尺寸限制，对称性假设或其他角度规律性，我们对$ u _+$进行物理空间随机化，并在$ v _+$上进行角度随机化，从而产生随机最终状态$（u _+^+^ω，v _++^ω）$。我们几乎每$ω$都可以获得它，Zakharov系统散射到最终状态$（u _+^ω，v _+^ω）$都有独特的解决方案。证据中的关键成分是使用时间加权规范和广义的strichartz估计值，由于随机化而可访问。
We consider the final-state problem for the Zakharov system in the energy space in three space dimensions. For $(u_+, v_+) \in H^1 \times L^2$ without any size restriction, symmetry assumption or additional angular regularity, we perform a physical-space randomization on $u_+$ and an angular randomization on $v_+$ yielding random final states $(u_+^ω, v_+^ω)$. We obtain that for almost every $ω$, there is a unique solution of the Zakharov system scattering to the final state $(u_+^ω, v_+^ω)$. The key ingredient in the proof is the use of time-weighted norms and generalized Strichartz estimates which are accessible due to the randomization.
