<p style='text-indent:20px;'>This paper focuses on two-dimensional incompressible non-resistive MHD equations with only horizontal dissipation in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{T}\times\mathbb{R} $\end{document}</tex-math></inline-formula>. Invoking three Poincaré-type inequalities about the derivative, we study global well-posedness of...

Horizontal wells can significantly improve the gas production and are expected to be an efficient exploitation method for industrialization of natural hydrates (NGHs) in future. However, near-wellbore hydrate is highly prone decomposition during drilling process, owing disturbance aroused by factors such as fluid temperature, pressure, salinity. These issues result engineering accidents bit sti...

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...

    The combination of horizontal drilling along with hydraulic fracturing has significantly improved the production of hydrocarbon reservoirs and made it possible to extract the relatively impermeable and uneconomical reservoirs. The production rate of oil and gas wells increases proportional to hydraulic fracture aperture or crack opening displacement (COD). This is an important parameter i...