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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2501.02697 |
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| _version_ | 1866929660188688384 |
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| author | Lee, Yoonjung |
| author_facet | Lee, Yoonjung |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The 3D energy-critical inhomogeneous nonlinear Schrodinger equation with strong singularity Lee, Yoonjung Analysis of PDEs Primary: 35A01, 35Q55, Secondary: 35B45 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. |
| title | The 3D energy-critical inhomogeneous nonlinear Schrodinger equation with strong singularity |
| topic | Analysis of PDEs Primary: 35A01, 35Q55, Secondary: 35B45 |
| url | https://arxiv.org/abs/2501.02697 |