Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912547437805568 |
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| author | Kumar, Vishvesh Mondal, Shyam Swarup Sitiraju, Iswarya Song, Manli |
| author_facet | Kumar, Vishvesh Mondal, Shyam Swarup Sitiraju, Iswarya Song, Manli |
| contents | In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schrödinger equations with power-type nonlinearities. In addition, we extend our analysis to the Dunkl Schrödinger equations under partial regularity, defined with respect to two distinct root systems. This extension poses significant challenges, mainly due to the lack of a suitable stationary phase method in the Dunkl setting. To overcome this difficulty, we develop a new result that provides an adaptation of the stationary phase method to the framework of Dunkl analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for higher order Schrödinger equations with Partial regular initial data Kumar, Vishvesh Mondal, Shyam Swarup Sitiraju, Iswarya Song, Manli Analysis of PDEs Functional Analysis Primary 35E15, 42C10, Secondary 35Q55, 35L70, 35B65 In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schrödinger equations with power-type nonlinearities. In addition, we extend our analysis to the Dunkl Schrödinger equations under partial regularity, defined with respect to two distinct root systems. This extension poses significant challenges, mainly due to the lack of a suitable stationary phase method in the Dunkl setting. To overcome this difficulty, we develop a new result that provides an adaptation of the stationary phase method to the framework of Dunkl analysis. |
| title | Strichartz estimates for higher order Schrödinger equations with Partial regular initial data |
| topic | Analysis of PDEs Functional Analysis Primary 35E15, 42C10, Secondary 35Q55, 35L70, 35B65 |
| url | https://arxiv.org/abs/2508.15670 |