Asymptotics of solutions to the generalized Ostrovsky equation

作者：Hayashi Nakao^*; Naumkin Pavel I; Niizato Tomoyuki

来源：Journal of Differential Equations, 2013, 255(8): 2505-2520.

DOI：10.1016/j.jde.2013.07.001

• Ostrovsky equation
• Time decay
• Asymptotic behavior of solutions

We consider the Cauchy problem for the generalized Ostrovsky equation
u(tx) = u + (f(u))xx,
where f(u) = vertical bar u vertical bar(rho-1)u if rho is not an integer and f(u) = u(rho) if rho is an integer. We obtain the L-infinity time decay estimates and the large time asymptotics of small solutions under suitable conditions on the initial data and the order of the nonlinearity.

• 出版日期2013-10-15