论文标题
Zakharov System的无限尺寸符号能力和非尺寸的财产
Infinite dimensional symplectic capacity and nonsqueezing property for the Zakharov system on the $1$-dimensional torus
论文作者
论文摘要
我们证明了Zakharov系统在圆环上的符合能力的不变性。如果Zakharov解决方案图的定义明确，则可以将其视为符号切除型。因此，我们首先通过当地的适应性和保护定律来展示全球范围的良好性。可以使用近似方法获得符号能力的不变性。许多作者使用一种近似方法来获得非Queezing定理，而不是符号能力的不变性。但是，库克辛（Kuksin）引入的哈密顿系统的条件可以通过新的改良无限尺寸哈密顿系统放松。因此，我们可以回到包含非Queezing属性的合成能力。启发式上，我们通过使用Hamiltonian系统获得不变性，该系统在高频下具有线性流动和低频率的非线性流动。
We prove the invariant of the symplectic capacity for the Zakharov system on a torus. If the Zakharov solution map is well-defined, then it can be regarded as a symplectomorphism. Thus, we first show the global well-posedness via the local well-posedness and the conservation law. The invariant of the symplectic capacity can be obtained using an approximation method. Many authors use an approximation method to obtain the nonsqueezing theorem, instead of an invariant of the symplectic capacity. However, the conditions of the Hamiltonian system introduced by Kuksin can be relaxed by a new modified infinite dimensional Hamiltonian system. Thus we can back to the symplectic capacity which contains the nonsqueezing property. Heuristically, we obtain the invariant by using the Hamiltonian system which has linear flow at high frequencies and nonlinear flow at low frequencies.
