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.
UR - http://www.scopus.com/inward/record.url?scp=85012134612&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85012134612&partnerID=8YFLogxK
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 -