TY - JOUR
T1 - The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space
AU - Segata, Jun ichi
AU - Watanabe, Keishu
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - 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 │ → ∞.
AB - 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 │ → ∞.
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U2 - 10.1007/s00030-016-0405-y
DO - 10.1007/s00030-016-0405-y
M3 - Article
AN - SCOPUS:84983801284
SN - 1021-9722
VL - 23
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 5
M1 - 51
ER -