Global existence and uniqueness of solutions to the initial boundary value problem of 3D Navier–Stokes equations with Cattaneo law

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In this paper, we prove the global existence and uniqueness of solutions to the initial boundary value problem of 3D Navier–Stokes equations with Cattaneo law for viscous heat-conductive gas. We know that the change in the heat conduction law affects the energy equation directly, so the key is to prove the existence of the solution of the linear energy equation. To prove the key point, we make great use of the idea about positive definite matrix by the properties and related theorem of parabolic linear equations.