非均匀介质中Zakharov系统的位力奇性解

Virial Type Singular Solutions to Zakharov System in Nonhomogeneous Medium

研究非均匀介质中Zakharov系统的位力奇性解.该系统描述了静电势与等离子密度在静电极限意义下的相互作用.一方面,利用位力恒等式,在c_0=+∞时证明了所研究的Zakharov系统的有限时间爆破结果.另一方面,通过建立局部的位力恒等式并利用关于时间的Lyapunov函数的存在性,在0<c_0<+∞时得到了所研究的Zakharov系统具负能量的径向对称解的爆破结果.

The author studies virial type singular solutions to the Zakharov system in a nonhomogeneous medium, the system describes the interaction of the electrostatic potential with the plasma density in the sense of electrostatic limit. By using a virial identity, the author proves a finite time blow-up result of the Zakharov system for co = ＋∞. Also the author obtains a blow-up result of the radially symmetric solution with negative energy to the Zakharov system for 0 〈 C0 〈 ＋∞by establishing a local virial identity and using the existence of a Lyapunov function in time.