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Recently, Niche [J. Differential Equations, 260 (2016), 4440–4453] established upper bounds on the decay rates of solutions to the 3D incompressible Navier–Stokes–Voigt equations in terms of the decay character r ∗ of the initial data in H 1 (R 3). Motivated by this work, we focus on characterizing the large-time behavior of all space-time derivatives of the solutions for the 2D case and establish upper bounds and lower bounds on their decay rates by making use of the decay character and Fourier splitting methods. In particular, for the case − n 2 < r ∗ ⩽ 1 , we verify the optimality of the upper bounds, which is new to the best of our knowledge. Similar improved decay results are also true for the 3D case. [ABSTRACT FROM AUTHOR]

In this paper, we make the first attempt to figure out the differences on Hölder regularity in time of solutions and conserved physical quantities between the ideal electron magnetohydrodynamic equations concerning Hall term and the incompressible Euler equations involving convection term. It is shown that the regularity in time of magnetic field B is C_{t}^{\frac {\alpha }2} provided it belongs to L_{t}^{\infty } C_{x}^{\alpha } for any \alpha >0, its energy is C_{t}^{\frac {2\alpha }{2-\alpha }} as long as B belongs to L_{t}^{\infty } \dot {B}^{\alpha }_{3,\infty } for any 0<\alpha <1 and its magnetic helicity is C_{t}^{\frac {2\alpha +1}{2-\alpha }} supposing B belongs to L_{t}^{\infty } \dot {B}^{\alpha }_{3,\infty } for any 0<\alpha <\frac 12, which are quite different from the classical incompressible Euler equations. [ABSTRACT FROM AUTHOR]

In this paper, we make the first attempt to investigate the Cauchy problem of a shallow water model, namely, the inviscid lake equations, in the Besov spaces. Notably, we prove the global existence and uniqueness of the solutions in the Besov spaces Bp,qs(ℝ2)$$ {B}_{p,q}&amp;#x0005E;s\left({\mathbb{R}}&amp;#x0005E;2\right) $$ for s>2p+1$$ s&gt;\frac{2}{p}&amp;#x0002B;1 $$ and s=2p+1$$ s&amp;#x0003D;\frac{2}{p}&amp;#x0002B;1 $$ if q=1$$ q&amp;#x0003D;1 $$, which contain the particular case of the endpoint Besov space B∞,11(ℝ2)$$ {B}_{\infty, 1}&amp;#x0005E;1\left({\mathbb{R}}&amp;#x0005E;2\right) $$. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system by imposing natural boundary conditions and regularity assumptions on the initial data, without any compatibility condition. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response α and the viscosity ν vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of ν , α and the radius of the family of spatial domains. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the Hölder regularity in time of both solutions and their energy for the generalized surface quasi-geostrophic equation with the velocity v given by v = R ⊥ Λ γ − 1 θ. In the first part, it is shown that the regularity in time of solutions θ is C t α for 0 < α < 1 with 0 < γ ≤ 1 and C t α / γ for γ − 1 < α < 1 with 1 ≤ γ < 2 , as long as θ belongs to L t ∞ C x α . In the second part, we address the Hölder regularity in time of their energy and establish the corresponding criteria for the temperature in Onsager-subcritical spaces. [ABSTRACT FROM AUTHOR]