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<p>We conduct a mathematical investigation into the Cauchy problem of compressible Navier–Stokes system of non-Newtonian fluids with Bingham-type in this paper. We investigate the large-time behavior of classical solutions for the equations. More specifically, we construct the linearized system in terms of a combination of the solutions and we investigate the decay-in-time properties of the Cauchy problem for the system of 3D isentropic compressible Bingham fluid with the initial perturbation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\rho ^0, \varvec{v}^0)\)</EquationSource> </InlineEquation>. We give the time decay estimation of the solution for the equation after overcoming the difficulty caused by the nonlinear term in the mathematical model of Bingham fluid.</p>

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Large Time Behavior of Solutions to the Compressible Bingham Fluid Equations

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Jialiang Wang

摘要

We conduct a mathematical investigation into the Cauchy problem of compressible Navier–Stokes system of non-Newtonian fluids with Bingham-type in this paper. We investigate the large-time behavior of classical solutions for the equations. More specifically, we construct the linearized system in terms of a combination of the solutions and we investigate the decay-in-time properties of the Cauchy problem for the system of 3D isentropic compressible Bingham fluid with the initial perturbation \((\rho ^0, \varvec{v}^0)\) . We give the time decay estimation of the solution for the equation after overcoming the difficulty caused by the nonlinear term in the mathematical model of Bingham fluid.