We consider the generalized Korteweg-de Vries (gKdV) equation with the time oscillating nonlinearity: ∂tu + ∂x 3u + g(ωt)∂x(│u│p−1u) = 0, (t, x) ∈ R × R. Under the suitable assumption on g, we show that if the nonlinear term is mass critical or supercritical i.e., p≥ 5 and u(0)∈Ḣsp , where sp= 1 / 2 - 2 / (p- 1) is a scale critical exponent, then there exists a unique global solution to (gKdV) provided that | ω| is sufficiently large. We also obtain the behavior of the solution to (gKdV) as │ ω │ → ∞.
- Generalized Korteweg-de Vries equation
ASJC Scopus subject areas
- Applied Mathematics