论文标题
爆炸和散射标准以上高于阈值的焦点非均匀的非线性schrödinger方程
Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation
论文作者
论文摘要
我们考虑$ \ Mathbb {r}^n $，$ n \ geq 1 $，$ n \ geq 1 $，$ i \ partial_t u + +ΔU + + e + e + e + e + e + | x | x | x |^{ - b} | h^1（\ mathbb {r}^n）$。我们扩展了散射和爆炸之间的二分法，以使质量能阈值（并任意能量）上方的溶液。我们还显示了其他两个爆炸标准，即鉴于当地适应性良好，WICH在任何质量危险环境中都是有效的。
We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $\mathbb{R}^N$, $N \geq 1$, $$i \partial_t u + Δu + |x|^{-b} |u|^{p-1}u = 0,$$ with finite-variance initial data $u_0 \in H^1(\mathbb{R}^N)$. We extend the dichotomy between scattering and blow-up for solutions above the mass-energy threshold (and with arbitrarily large energy). We also show other two blow-up criteria, wich are valid in any mass-supercritical setting, given there is local well-posedness.
