Varlamov, V.; Liu, Yue Cauchy problem for the Ostrovsky equation. (English) Zbl 1059.35035 Discrete Contin. Dyn. Syst. 10, No. 3, 731-753 (2004). Summary: Considered herein is an initial-value problem for the Ostrovsky equation that arises in modelling the unidirectional propagation of long waves in a rotating homogeneous incompressible fluid. Nonlinearity and dispersion are taken into account, but dissipation is ignored. Local- and global-in-time solvability is investigated. For the case of positive dispersion a fundamental solution of the Cauchy problem for the linear equation is constructed, and its asymptotics is calculated as \(t\to\infty\), \(x/t=\text{const}\). For the nonlinear problem solutions are constructed in the form of a series and the analogous long-time asymptotics is obtained. Cited in 47 Documents MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 35B40 Asymptotic behavior of solutions to PDEs 35B65 Smoothness and regularity of solutions to PDEs 35C10 Series solutions to PDEs 35C20 Asymptotic expansions of solutions to PDEs Keywords:dispersion; no dissipation; unidirectional propagation of long waves; rotating homogeneous incompressible fluid; Local- and global-in-time solvability PDF BibTeX XML Cite \textit{V. Varlamov} and \textit{Y. Liu}, Discrete Contin. Dyn. Syst. 10, No. 3, 731--753 (2004; Zbl 1059.35035) Full Text: DOI