The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ > 3 2 and constant viscosity c...

Multiple Solutions: A Key to Strengthening the Generalization Skill in Mathematic-Like Thinking   Z. Rahimi* E. Talaa'ee, Ph.D.** E. Reyhaani, Ph.D.*** H. Fardaanesh, Ph.D.****   Emphasizing multiple solutions can help with the strengthening of the generalization skill. To test this hypothesis, a group of high school students in math and experimental sciences was selected in or...

We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained.

Food proteins have long been recognized for their nutritional and functional properties. The nutritional properties of proteins are associated with their amino acid content. On the other hand, the functional properties of proteins relate to their contribution to the physiochemical and sensory properties of foods (Sila and Bougatef, 2016). Marine organisms contain proteins with high quantities o...

The weak formulation of moving boundary problems with possibly vanishing specific heat, that is governed by parabolic and/or elliptic differential equations, is developed. The uniqueness of the resulting weak solution is then proved. This approach is used to obtain numerical solutions to some physical examples, which arise in electrochemical machining processes, and in saturated / unsaturated f...

We consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. When the initial density function ρ0 has a positive lower bound, we obtain the existence and uniqueness of global classical, and strong solutions and the existence of weak solutions. For ρ0 ≥ 0, we obtain the existence of global strong solutions.

We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are Hölder continuous near boundary provided that either the scaled L x,t-norm of the velocity with 3/p+ 2/q ≤ 2, 2 < q <∞, or the scaled L x,t-norm of the vorticity with 3/p+ 2/q ≤ 3, 2 < q <∞ are sufficiently small near th...