论文标题
Zakharov系统的最小非散发解决方案
Minimal non-scattering solutions for the Zakharov system
论文作者
论文摘要
我们认为Zakharov系统在能量临界维度$ d = 4 $中，能量低于基态。众所周知，基态溶液在全球范围内及时存在，并在径向情况下散射。在非统治情况下，在基态下方的散射是一个悬而未决的问题。我们表明，如果散射失败，则在基态以下存在最小能量的非散射溶液。此外，该解决方案的轨道是预发模量翻译。证明是由浓度紧凑的参数，以及用于分散溶液的精制小数据理论。
We consider the Zakharov system in the energy critical dimension $d=4$ with energy below the ground state. It is known that below the ground state solutions exist globally in time, and scatter in the radial case. Scattering below the ground state in the non-radial case is an open question. We show that if scattering fails, then there exists a minimal energy non-scattering solution below the ground state. Moreover the orbit of this solution is precompact modulo translations. The proof follows by a concentration compactness argument, together with a refined small data theory for energy dispersed solutions.
