On a Boussinesq capillarity system: Hamiltonian reductions and associated quartic geometries. (English) Zbl 1290.35207

Rogers, C.; Schief, W. K.

Stud. Appl. Math. 132, No. 1, 1-12 (2014).

The authors deal with the nonlinear Boussinesq capillarity system which may be derived from the L. K. Antanovskii model [“Microscale theory of surface tension”, Phys. Rev. E. 54, 6285–6290 (1996)] in one case of one-parameter free-energy laws. The application of a quartic ansatz for the density distribution leads to Hamiltonian reductions associated with isopycnal geometries: in \(2+1\) dimension with time-modulated Cassini ovals and in \(3+1\) dimension with time-modulated “red blood cell” geometries [B. Angelov and I. M. Mladenov, in: Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, 1999. Sofia: Coral Press Scientific Publishing. 27–46 (2000; Zbl 0970.92009)]. Thus it is shown that the considered nonlinear Boussinesq-type capillarity model system allows exact reduction to coupled Hamiltonian subsystems.

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC:

35Q35	PDEs in connection with fluid mechanics
35Q55	NLS equations (nonlinear Schrödinger equations)
76D45	Capillarity (surface tension) for incompressible viscous fluids
76A05	Non-Newtonian fluids

Keywords:

Boussinesq-type capillarity; exact reductions to Hamiltonian subsystems

Citations:

Zbl 0970.92009

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