The mixed fractional Hartree equations in Fourier amalgam and modulation spaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911078672236544 |
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| author | Bhimani, Divyang G. Hajaiej, Hichem Haque, Saikatul |
| author_facet | Bhimani, Divyang G. Hajaiej, Hichem Haque, Saikatul |
| contents | We prove local and global well-posedness for mixed fractional Hartree equation and with low regularity Cauchy data in Fourier amalgam $\F W(L^p,\ell^q)$ and modulation $M^{p,q}$ spaces. Similar results also hold for the Hartree equation with harmonic potential in some modulation spaces. Our approach also addresses Hartree-Fock equations of finitely many (but arbitrary large) particles. A key ingredient of our method is to establish trilinear estimates for Hartree non-linearity and the use of Strichartz estimates. As a consequence, we could gain $\F W(L^p,\ell^q)$ and $M^{p,q}-$regularity for all $p,q\in [1, \infty].$ In particular, we extend result of Bhimani-Grillakis-Okoudju \cite{bhimani2020hartree} in $M^{p,q}$ for all $p,q$ and complement known results in Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_10683 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The mixed fractional Hartree equations in Fourier amalgam and modulation spaces Bhimani, Divyang G. Hajaiej, Hichem Haque, Saikatul Analysis of PDEs 35Q40, 35Q55, 42B35, 35B30, 35A01 We prove local and global well-posedness for mixed fractional Hartree equation and with low regularity Cauchy data in Fourier amalgam $\F W(L^p,\ell^q)$ and modulation $M^{p,q}$ spaces. Similar results also hold for the Hartree equation with harmonic potential in some modulation spaces. Our approach also addresses Hartree-Fock equations of finitely many (but arbitrary large) particles. A key ingredient of our method is to establish trilinear estimates for Hartree non-linearity and the use of Strichartz estimates. As a consequence, we could gain $\F W(L^p,\ell^q)$ and $M^{p,q}-$regularity for all $p,q\in [1, \infty].$ In particular, we extend result of Bhimani-Grillakis-Okoudju \cite{bhimani2020hartree} in $M^{p,q}$ for all $p,q$ and complement known results in Sobolev spaces. |
| title | The mixed fractional Hartree equations in Fourier amalgam and modulation spaces |
| topic | Analysis of PDEs 35Q40, 35Q55, 42B35, 35B30, 35A01 |
| url | https://arxiv.org/abs/2302.10683 |