Steady periodic rotational gravity waves with negative surface tension

作者：Fan, Lili; Gao, Hongjun^*

来源：Japan Journal of Industrial and Applied Mathematics, 2017, 34(2): 531-554.

DOI：10.1007/s13160-017-0256-x

• Rotational gravity waves
• Surface tension
• Local bifurcation
• Global bifurcation
• Symmetry

Consideration in this paper is the two-dimensional steady periodic rotational gravity waves with negative surface tension. Local curves of small amplitude solutions of the resulting problem are obtained by using the Crandall-Rabinowitz local bifurcation theory. By means of the global bifurcation theory combined with the Schauder theory of elliptic equations with the Venttsel boundary conditions, the curves of small amplitude solutions is extended to the global continuum of solutions. Furthermore, it is shown that those waves are necessarily symmetric about the crest under the assumption that their surface profiles are monotonic between troughs and crests and locally strictly monotonic near the troughs.

• 出版日期2017-8
• 单位吉林大学; 河南师范大学; 南京师范大学