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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6540| Title: | Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity |
| Authors: | BHIMANI, DIVYANG G. Haque, Saikatul Dept. of Mathematics |
| Keywords: | BBM equation Ill-posedness Fourier amalgam spaces Wiener amalgam spaces Fourier-Lebesgue spaces Modulation spaces 2022-JAN-WEEK4 TOC-JAN-2022 2021 |
| Issue Date: | Dec-2021 |
| Publisher: | MDPI |
| Citation: | Mathematics, 9(23), 3145. |
| Abstract: | We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut ` ux ` uux ´ uxxt “ 0,px, tq P M ˆ R where M “ T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthens several known NI results at zero initial data in Hs pTq established by Bona– Dai (2017) and the ill-posedness result established by Bona–Tzvetkov (2008) and Panthee (2011) in Hs pRq. Our result is sharp with respect to the local well-posedness result of Banquet–Villamizar–Roa (2021) in modulation spaces M2,1 s pRq for s ě 0 |
| URI: | https://doi.org/10.3390/math9233145 http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6540 |
| ISSN: | 2227-7390 |
| Appears in Collections: | JOURNAL ARTICLES |
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