TY - JOUR

T1 - Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

AU - Bernal-Vílchis, Fernando

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

N1 - Publisher Copyright:
© 2017 Fernando Bernal-Vílchis et al.

PY - 2017

Y1 - 2017

N2 - We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂ x ∂ t u - b / 3 ∂ x 3 u - ∂ x K u 3 = a u, t, x ℝ 2, u 0, x = u 0 x, xR, where a b > 0. Define 0 = 27 a / b 1 / 4. Suppose that K is a pseudodifferential operator with a symbol K ^ such that K ^ ± 0 = 0, I mK ^ = 0, and K ^ ≤ C. For example, we can take K^ = 2 - 0 2 / 2 + 1. We prove the global in time existence and the large time asymptotic behavior of solutions.

AB - We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂ x ∂ t u - b / 3 ∂ x 3 u - ∂ x K u 3 = a u, t, x ℝ 2, u 0, x = u 0 x, xR, where a b > 0. Define 0 = 27 a / b 1 / 4. Suppose that K is a pseudodifferential operator with a symbol K ^ such that K ^ ± 0 = 0, I mK ^ = 0, and K ^ ≤ C. For example, we can take K^ = 2 - 0 2 / 2 + 1. We prove the global in time existence and the large time asymptotic behavior of solutions.

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U2 - 10.1155/2017/3879017

DO - 10.1155/2017/3879017

M3 - Article

AN - SCOPUS:85012134612

SN - 1687-9643

VL - 2017

JO - International Journal of Differential Equations

JF - International Journal of Differential Equations

M1 - 3879017

ER -