Energy equality for the 3D critical convective Brinkman–Forchheimer equations
By Karol W. Hajduk, James C. Robinson. 2016
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Abstract In this paper we give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman–Forchheimer equations (also called in the literature the tamed Navier–Stokes equations) ∂ t u − μ Δ u + ( u ⋅ ∇ ) u + ∇ p + α u + β | u | r − 1 u = 0 on a 3D periodic domain, for values of the absorption exponent r larger than 3. Furthermore, we prove that global, regular solutions exist also for the critical value of exponent r = 3 , provided that the coefficients satisfy the relation 4 μ β ≥ 1 . Additionally, we show that in the critical case every weak solution verifies the energy equality and hence is continuous into the phase space L 2 . As an application of this result we prove the existence of a strong global attractor, using the theory of evolutionary systems developed by Cheskidov.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a67f0af967c94e47d098aaaa1c1340bae053a6d
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces (2019, methodology): “1Department of Mathematics, Princeton University, Princeton, New Jersey, USA 2Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland 3Mathematics Institute, Zeeman Building, University of Warwick, Coventry, UK Correspondence James C. Robinson, Mathematics Institute, Zeeman Building, Un”