Blowup in stagnation-point form solutions of the inviscid 2d Boussinesq equations

Blowup in stagnation-point form solutions of the inviscid 2d Boussinesq equations

The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth nontrivial initial velocities in stagnation-point form solutions of this system is established. On an infinite strip = {(x, y) ∈ [0, 1] × R+}, we consider velociti...

The 2D Incompressible Boussinesq Equations

An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time ...

Explicit Solutions of Generalized Nonlinear Boussinesq Equations

By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components. The decomposition series analytic solution of the problem is quickly obtained by observing the existence ...

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 ...