Asymptotic Behavior of Solutions to a New Hall-MHD System

On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect

“…Moreover, by using the properties of decay character and the Fourier splitting method, one also shows the optimal decay rates for higher order time and spatial derivatives of solutions. In a sense, the results of this paper can be seen as an improvement of the previous results in [11,29,30].…”

“…Combining the results of Niche [23], Niche et al [27], Anh et al [33], Zhao [30], we obtain the following three lemmas:…”

“…From a mathematical point of view, the local well-posedness, global well-posedness and large time behavior of solutions are very interesting. In the previous works of Fan et al [11], the authors studied the local well-posedness of strong solutions and gave the preliminary result on the small initial data global well-posedness; Zhao [29,30] considered the large time behavior of solutions, established the decay estimates for the weak solution (see also Lemma 1) and the strong solution (see Lemma 2). In this paper, one only assumes that u 0 H 3 2 +ε + b 0 H 2 is sufficiently small, obtains the global well-posedness of strong solution and establishes the a priori estimates on higher order time and spatial derivatives of solutions.…”

The Temporal decay rate of solutions to 2D dissipative quasi-geostrophic flows

“…There's also a lemma on the relation between the decay character of Λ s v 0 and that of v 0 . 1,28]). The decay character r * = r * (v 0 ) measure the "order" of v 0 (ξ) at ξ = 0 in frequency space.…”

“…Proof. Applying ∂ p t to system (1) 1 , multiplying both side by ∂ p t θ, integrating over R 2 , we arrive at (28) 1 2…”