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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02697 |
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Table of Contents:
- In this paper, we study the Cauchy problem for the 3D energy-critical inhomogeneous nonlinear Schrödinger equation(INLS) $$i\partial_{t}u+Δu=\pm|x|^{-α}|u|^{4-2α}u$$ with strong singularity $3/2\leq α<2$. The well-posedness problem is well-understood for $0<α<3/2$, but the case $3/2\leq α<2$ has remained open so far. We address the local/small data global well-posedness result for $3/2\leq α<11/6$ by improving the inhomogeneous Strichartz estimates on the weighted space.