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In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For 0<s,t<1,p>0, if u and v satisfy the following nonlinear system -Δpsux=fvx;  -Δptvx=gux,  x∈B10;  ux,vx=0,  x∉B10. and f,g are nonnegative continuous functions satisfying the following: (i) f(r) and g(r) are increasing for r>0; (ii) f′(r)/rp-2, g′(r)/rp-2 are bounded near r=0. Then the positive solutions (u,v) must be radially symmetric and monotone decreasing about the origin.

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressurepin the homogeneous Besov spaceḂ∞,∞0.

In this paper we consider the following system of fractional nonlinear equations in the half space R

Greenhouse gas emissions cause many global problems. Under the strong promotion of the government’s two-carbon goals policy, China’s petroleum industry is actively carrying out the application of carbon capture, utilization, and storage (CCUS). The energy consumption and carbon emissions in China are reviewed, and the importance of the petroleum industry in the process of carbon emission reduction is clarified. The applications, advantages, and disadvantages of carbon capture, carbon utilization, and carbon sequestration technologies in China’s petroleum industry are summarized, respectively. The current challenges and risks faced by China’s petroleum industry in the operation of CCUS projects are analyzed, and corresponding suggestions are provided. This article aims to systematically provide references and help for the application of CCUS in China’s petroleum industry.