Physics

Nonlinear system

Mathematics

Boundary (topology)

Reaction–diffusion system

Epistemology

Regular polygon

Convex optimization

Mathematical analysis

Philosophy

Neumann boundary condition

A priori estimate

Subderivative

Geometry

Weak solution

Quantum mechanics

A priori and a posteriori

Backward Euler method

Compressibility

Applied mathematics

Euler equations

Thermodynamics

Scientia Sinica Mathematica

In this paper, we consider a new class of a dynamic system which couplesa nonstationary incompressible Navier-Stokes equation involving nonmonotone and multivalued boundary 条件 of subdifferential type,and a generalized quasilinear reaction-diffusion equation with the Neumann boundary condition.The variational formulation of the system is provided in the form of an evolutionary hemivariational inequality coupled with the nonlinear parabolic equation. The main result concerning with the existence of global weak solutions to the system is proved.Firstly, the backward Euler technique and the feedback iterative method are used to develop a temporally semi-discrete approximate 问题. Next, invoking a surjectivity result for weakly-weakly upper semicontinuous multivalued operators, the existence and $a$ $priori$ estimates for the 解 to the semi-discrete approximate 问题 are established. Finally, using a limiting procedure for solutions to the approximate 问题, a 定理 on the existence of weak solutions to the system is obtained.

Nonstationary incompressible Navier-Stokes system governed by a quasilinear reaction-diffusion equation