HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

Abstract

Abstract: We show the existence of dissipative Hölder continuous solutions of the Boussinesq equations. More precise, for any β ∈ (0, 1/5), a time interval[0, T] and any given smooth energy profile e:[0, T] → (0, ∞), there exist a weak solution (v, θ) of the 3d Boussinesq equations such that (v, θ) ∈ C^β(T³×[0, T]) with e(t)=∫_T³|v(x, t)|²dx for all t ∈[0, T]. This extend the result of [2] about Onsager's conjecture into Boussinesq equation and improve our previous result in [30].

Key words: Boussinesq equations, Hölder continuous solutions, prescribed kinetic energy

Tao TAO, Liqun ZHANG. HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS[J].Acta Mathematica Scientia, 2018, 38(5): 1591-1616.

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