论文标题
扎卡罗夫系统以下的全球良好性扎克哈罗夫系统
Global wellposedness for the energy-critical Zakharov system below the ground state
论文作者
论文摘要
考虑到Zakharov系统的凯奇问题，在能量临界维度$ d = 4 $中。我们证明，对于任何初始数据，能量和波浪质量以下的所有初始数据都在完全的（非radial）能量空间中占据整个（非radial）的能量。结果是基于具有潜力的Schrödinger方程的Strichartz估计值。更确切地说，对于任何潜在的解决质量以低于基态限制的质量的潜在，均一的估计值均匀地保持。关键的新成分是双线性（伴随）傅立叶限制估计，用于在双端点strichartz空间中强迫不均匀的schrödinger方程解决方案。
The Cauchy problem for the Zakharov system in the energy-critical dimension $d=4$ is considered. We prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a Strichartz estimate for the Schrödinger equation with a potential. More precisely, a Strichartz estimate is proved to hold uniformly for any potential solving the free wave equation with mass below the ground state constraint. The key new ingredient is a bilinear (adjoint) Fourier restriction estimate for solutions of the inhomogeneous Schrödinger equation with forcing in dual endpoint Strichartz spaces.
