自相似波映射的谱性质和线性稳定性
Spectral Properties and Linear Stability of Self-Similar Wave Maps
摘要：
研究了从$(3+1)$ -Minkowski空间到三球$S^3$的共旋波映射.已知存在可数族$\{f_n\}$自相似解。利用算子理论的方法研究了它们在线性扰动下的稳定性。为此，我们研究了扰动算子的谱，证明了相应的线性柯西问题的适定性，并推导出解的增长估计。最后，我们研究了由$f_n$得到的极限解的扰动，它是通过令$n \to \infty$ .
英文摘要：
We study co--rotational wave maps from $(3+1)$--Minkowski space to the three--sphere $S^3$. It is known that there exists a countable family $\{f_n\}$ of self--similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well--posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from $f_n$ by letting $n \to \infty$.
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