scholarly journals Energy Conservation for 3D Tropical Climate Model in Periodic Domains

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Hui Zhang
Keyword(s):  
Energy Conservation ◽  
Euler Equations ◽  
Weak Solutions ◽  
Climate Model ◽  
Sufficient Conditions ◽  
Tropical Climate ◽  
Tropical Climate Model ◽  
Periodic Domains ◽  
Onsager’S Conjecture

In this paper, we prove the energy conservation for the weak solutions of the 3D tropical climate model under some sufficient conditions. Our results are similar to Onsager’s conjecture which is on energy conservation for weak solutions of Euler equations.

On Onsager's Conjecture

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Euler Equations ◽  
Weak Solutions ◽  
Time Derivative ◽  
Space Time ◽  
Spatial Derivative ◽  
Time Intervals ◽  
Higher Regularity ◽  
Onsager’S Conjecture

This chapter deals with Onsager's conjecture, which would be implied by a stronger form of Lemma (10.1). It considers what could be proven assuming Conjecture (10.1) by turning to Theorem 13.1, which states that for every δ‎ > 0, there exist nontrivial weak solutions (v, p) to the Euler equations on ℝ x ³. Here the energy will increase or decrease in certain time intervals. In order to determine which Hölder norms stay under control during the iteration, the chapter observes that the bound for the spatial derivative of the corrections V and P also controls their full space-time derivative. The chapter also discusses higher regularity for the energy, written as a sum of energy increments.

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