Decay rate of solutions to 3D Navier–Stokes–Voigt equations in Hm spaces

Decay characterization of solutions to the viscous Camassa–Holm equations

“…To weaken the condition v 0 ∈ L 1 , Bjorland and Schonbek [5] introduced a new idea in this area, by associating to a large class of L 2 -functions v 0 ∈ L 2 a decay character r * = r * (v 0 ), which measures the 'order' of v0 (ξ) at ξ = 0 in frequency space. In [17], Niche used this definition and characterized the decay rate of solutions to the Navier-Stokes-Voigt equations and studied the long-time behavior of its solutions by comparing them to solutions of the linear part; see also [3,26] for related results. In [18], Niche and Schonbek refined and extended Bjorland and Schonbek's work, more precisely, they defined the decay character of Λ s v 0 for v 0 ∈ H s (R n ), Λ = (−∆) 1/2 , s 0, and established its relation with the decay character of v 0 .…”

Global well-posedness and large time behavior of epitaxy thin film growth model

“…In 2015, Agélas [1] studied the global regularity of solutions for the Cauchy problem (1)-( 2) in 1D and 2D cases. The author assumed that the condition ν 2 ν 3 > ν 2 4 proved the existence and uniqueness of global strong solutions for problem (1)- (2). In this paper, we continue this research and study the global well-posedness of solutions for problem (1)-( 2) in R d with d ≥ 3.…”

“…In this section, we consider the temporary decay rate of strong solutions of problem ( 1)- (2) provided that Theorem 1.2 holds. First of all, one need to derive the evolution of the negative Sobolev norms of solution to problem (13) (which is equivalent to problem (1)-( 2)).…”

Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces

“…[2,14,16,17,20,24,26,27]). We also refer the interested reader to [3,19,28] for recent results on the time decay rates of solutions to the NSV equations in the whole space R 3 .…”