Novel Lower Bounds on the Radius of Spatial Analyticity for the KdV Type Equations
DOI:
https://doi.org/10.5890/JAND.2024.12.001Abstract
In this article, using multi-linear estimate in Bourgain type spaces, we prove the local well-posedness of initial value problem associated with the equation $\partial_{t}w +\partial_{x}^{3}w +\eta(t) \mathcal{L}w+\partial_{x}(w)^{k} = 0,$ $ k=2, 4 $. The solution is established on the line for analytic initial data $u_{0}$ that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improve earlier results in [1].References
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