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Local well-posedness and global analyticity for solutions of a generalized 0-equation
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 5 / October 2023
- Published online by Cambridge University Press:
- 27 September 2022, pp. 1630-1650
- Print publication:
- October 2023
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- Article
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In this work we study the Cauchy problem in Gevrey spaces for a generalized class of equations that contains the case $b=0$
of the $b$
-equation. For the generalized equation, we prove that it is locally well-posed for initial data in Gevrey spaces. Moreover, as we move to global well-posedness, we show that for a particular choice of the parameter in the equation the local solution is global analytic in both time and spatial variables.
