Global persistence of geometrical structures for the boussinesq equation with no diffusion

2016/03/24 by Danchin, Raphaël, Zhang, Xin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.07479

Abstract

Here we investigate the so-called temperature patch problem for the incompressible Boussinesq system with partial viscosity, in the whole space ℝ^N (N ≥ 2), where the initial temperature is the characteristic function of some simply connected domain with C^{1, ε} Hölder regularity. Although recent results in [1, 15] ensure that an initially C¹ patch persists through the evolution, whether higher regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue globally in time, in the 2-D case for large initial data and in the higher dimension case for small initial data.

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