Author:
Mucha Piotr B.,Xue Liutang
Abstract
AbstractThe paper analyzes the Navier–Stokes system coupled with the convective-diffusion equation responsible for thermal effects. It is a version of the Boussinesq approximation with a heat source. The problem is studied in the two dimensional plane and the heat source is a measure transported by the flow. For arbitrarily large initial data, we prove global in time existence of unique regular solutions. Measure being a heat source limits regularity of constructed solutions and it requires a non-standard framework of inhomogeneous Besov spaces of the $$L^\infty (0,T;B^s_{p,\infty })$$
L
∞
(
0
,
T
;
B
p
,
∞
s
)
-type. The uniqueness of solutions is proved by using the Lagrangian coordinates.
Funder
Narodowe Centrum Nauki
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
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