Nonlocal KdV Dynamics with Fractional Bessel Slope

Abstract

We study a one-dimensional nonlocal dispersive equation combining Airy dispersion, Helmholtz averaging, and a slope filtered by a fractional Bessel operator. For fractional orders from zero to one half, the nonlinear vector field is locally Lipschitz on the natural energy space, including the endpoint case. A contraction argument based on the Airy group gives local well-posedness, uniqueness, and locally Lipschitz dependence on the initial data. Conservation of a coercive quadratic energy is justified for mild solutions by resolvent regularization. Consequently, every real-valued energy-space solution exists globally.