Existence of periodic solutions of Boussinesq system

Analyticity of Periodic Solutions of the 2D Boussinesq System

The Cauchy problem for the 2D Boussinesq system with periodic boundary conditions is studied. The global existence and uniqueness of a solution with initial data (u(0), θ(0)) ∈ Φ(α) is established, where Φ(α) is the space of functions the kth Fourier coefficients of which decay at infinity as 1 |k|α , α > 2. It is proved that the solution becomes analytic at any positive time. Bibliography: 10 ...

Galerkin Approximations of Periodic Solutions of Boussinesq Systems

We consider the periodic initial-value problem for the family of a-b-c-d Boussinesq systems, [8], [9], and their completely symmetric analogs, [10]. We approximate their solutions by the standard Galerkin-finite element method using smooth periodic splines for discretizing in space. We prove optimal-order L error estimates for the resulting semidiscretizations. The numerical schemes are usual i...

Existence of Traveling-wave Solutions to Boussinesq Systems

In this manuscript, the existence of traveling-wave solutions to Boussinesq systems  ηt + ux + (ηu)x + auxxx − bηxxt = 0, ut + ηx + uux + cηxxx − duxxt = 0, is established. We prove that all the systems with a < 0, c < 0 and b = d exhibit traveling-wave solutions with small propagation speeds. The result complements our earlier work [6] on a restricted family of the systems where both existenc...

Existence and uniqueness of solutions for a periodic boundary value problem

In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY