Novel Lower Bounds on the Radius of Spatial Analyticity for the KdV Type Equations - Boukarou, Aissa; Guerbati, Kaddour; Zennir, Khaled; Mansouri, Aouatef (Journal of Applied Nonlinear Dynamics, 2026)
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 $\partial_{t}w +\partial_{x}^{3}w +η(t) \mathcal{L}w+\partial_{x}(w)^{k} = 0,$ $ 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].