论文标题
具有少量初始数据到具有能量超临界力量的半线性波方程的全球解决方案
Global Solutions with Small Initial Data to Semilinear Wave Equations with Energy Supercritical Powers
论文作者
论文摘要
考虑$ 1+n $尺寸半线性波方程，具有能量超危的能力$ p> 1+4/（n-2）$，我们在$ h^{s_c} \ times h^{s_c-1} $中获得任何初始数据的全球解决方案1/2+（n-3）/（2 \ max（n-1-p，n-3））$和$ s_c = n/2-2/（p-1）$。特别是，结合以前的作品，我们的结果对Strauss的猜想进行了完整的验证，最多可达空间尺寸$ 9 $。鉴于$ h^s $中良好的理论，较高维度的情况（$ n \ ge 10 $）似乎是无法实现的。
Considering $1+n$ dimensional semilinear wave equations with energy supercritical powers $p> 1+4/(n-2)$, we obtain global solutions for any initial data with small norm in $H^{s_c}\times H^{s_c-1}$, under the technical smooth condition $p>s_c-\bar{s}_0$, with $\bar{s}_0= 1/2+(n-3)/(2\max(n-1-p,n-3))$ and $s_c=n/2-2/(p-1)$. In particular, combined with previous works, our results give a complete verification of the Strauss conjecture, up to space dimension $9$. The higher dimensional case, $n\ge 10$, seems to be unreachable, in view of the wellposed theory in $H^s$.
