Almost optimal local well-posedness for modified Boussinesq equations
In this article, we investigate a class of modified Boussinesq equations, for which we provide first an alternate proof of local well-posedness in the space $(H^s\cap L^\infty)\times (H^s\cap L^\infty)(\mathbb{R})$ ($s\geq 0$) to the one obtained by Constantin and Molinet [7]. Secondly, we sho...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/24/abstr.html |
| Summary: | In this article, we investigate a class of modified Boussinesq equations,
for which we provide first an alternate proof of local well-posedness in
the space $(H^s\cap L^\infty)\times (H^s\cap L^\infty)(\mathbb{R})$ ($s\geq 0$)
to the one obtained by Constantin and Molinet [7].
Secondly, we show that the associated flow map is not smooth when considered
from $H^s\times H^s(\mathbb{R})$ into $H^s(\mathbb{R})$ for s<0,
thus providing a threshold for the regularity needed to perform a Picard
iteration for these equations. |
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| ISSN: | 1072-6691 |