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In order to better meet customer needs and respond to market demands more quickly, mounting number of manufacturing companies have begun to bid farewell to the traditional unitary manufacturing model. The collaborative manufacturing model has become a widely adopted manufacturing model for manufacturing companies. Aiming at the problem of partner selection for collaborative manufacturing of complex products in a collaborative supply chain environment, this paper proposes a multi-objective decision-making model that comprehensively considers the maximization of the matching degree of manufacturing capacity and the profits of supply chain, and gives the modeling process and application steps in detail. The method first uses fuzzy theory to evaluate the manufacturing capabilities of candidate collaborative manufacturing partners. Secondly, Vector Space Model (VSM) is used to calculate the matching degree of manufacturing capacity and manufacturing demand. Then, the paper studied the profit of the supply chain under the “non-cooperative” mechanism and the “revenue sharing” mechanism. Furthermore, the decision-making model is established. Finally, a simulation was carried out by taking complex product manufacturing of Gree enterprise as an example. The research results show the feasibility and effectiveness of the method.

It is well known that people can derive the radiation MHD model from an MHD-P1 approximate model. As pointed out by F. Xie and C. Klingenberg (2018), the uniform regularity estimates play an important role in the convergence from an MHD-P1 approximate model to the radiation MHD model. The aim of this paper is to prove the uniform regularity of strong solutions to an isentropic compressible MHD-P1 approximate model arising in radiation hydrodynamics. Here we use the bilinear commutator and product estimates to obtain our result.

In this work, we prove the local well-posedness of strong solutions to the compressible flow of a chemically reacting gaseous mixture with the initial data containing vacuum. Moreover, we should emphasize that there is no assuming compatibility condition on the initial data.

In this paper, we prove global well-posedness of strong solutions to a 1-D compressible non-isothermal model for nematic liquid crystals, provided that the initial datum satisfies a natural compatibility condition. The initial density may vanish in an open subset.

In this paper, we use the bootstrap argument to prove the uniform-in- k global strong solutions of the 2D density-dependent incompressible magnetic Benard problem in a bounded domain. Here k is the heat conductivity coefficient.

We prove the local well-posedness of strong solutions to a compressible full MHD-P1 approximate model arising in radiation magnetohydrodynamics with vacuum.

This paper proves the global well-posedness for the 2D Cahn-Hilliard-Boussinesq and a related system with partial viscous terms on bounded domains.

In this paper, we prove the local well-posedness of strong solutions to the density-dependent incompressible magneto-micropolar system with vacuum. There is no assuming compatibility condition on the initial data.

We prove the existence of strong global solutions of the 1-D modified compressible Navier-Stokes-Fourier equations proposed by Howard Brenner [1,2].