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This paper establishes a blowup criterion for the three-dimensional viscous, compressible, and heat conducting magneto-hydrodynamic (MHD) flows. It is essentially shown that for the Cauchy problem and the initial-boundary-value one of the three-dimensional compressible MHD flows with initial density allowed to vanish, the strong or smooth solution exists globally if the density is bounded from above and the velocity satisfies Serrin’s condition. Therefore, if the Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanishing or vacuum appearing in the non-vacuum region or even milder singularities) to form before the density becomes unbounded. This criterion is analogous to the well known Serrin’s blowup criterion for the three-dimensional incompressible Navier-Stokes equations, in particular, it is independent of the temperature and magnetic field and is just the same as that of the barotropic compressible Navier-Stokes equations. As a direct application, it is shown that the same result also holds for the strong or smooth solutions to the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, and heat conducting fluid.

In this paper, we construct a new suboptimal filter by deriving the Ito's stochastic differential equations of the estimation of higher order central moments satisfy and imposing some conditions to form a closed system. The essentially infinite-dimensional cubic sensor problem has been investigated in detail numerically to illustrate the reasonableness of the imposed conditions, and the numerical experiments support our discussion. A 2-dimensional polynomial filtering problem has also been experimented.

In this paper we propose a finite element time-domain method for modeling the optical black holes (OBHs) coupled with the perfectly matched layer (PML) technique. Stability analysis is carried out for the proposed scheme. Simulations of cylindrical, elliptical and square black holes demonstrate that our method is quite effective in modeling OBHs in time domain. To our best knowledge, this is the first OBHs simulation realized by the finite element time-domain method.

In this paper, we analyze the minimization of seminorms ∥L · ∥ on R^n under the constraint of a bounded I-divergence D(b,H·) for rather general linear operators H and L. The I-divergence is also known as Kullback–Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data but also in the case of multiplicative Gamma noise. Often H represents, e.g., a linear blur operator and L is some discrete derivative or frame analysis operator. A central part of this paper consists in proving relations between the parameters of I-divergence constrained and penalized problems. To solve the I-divergence constrained problem, we consider various first-order primal–dual algorithms which reduce the problem to the solution of certain proximal minimization problems in each iteration step. One of these proximation problems is an I-divergence constrained least-squares problem which can be solved based on Morozov’s discrepancy principle by a Newton method. We prove that these algorithms produce not only a sequence of vectors which converges to a minimizer of the constrained problem but also a sequence of parameters which converges to a regularization parameter so that the corresponding penalized problem has the same solution. Furthermore, we derive a rule for automatically setting the constraint parameter for data corrupted by multiplicative Gamma noise. The performance of the various algorithms is finally demonstrated for different image restoration tasks both for images corrupted by Poisson noise and multiplicative Gamma noise.