This paper investigates the space-time decay properties of solutions to the compressible Navier-Stokes equations with hyperbolic heat conduction in the whole space \({\mathbb {R}}^3\) . By employing weighted Sobolev space techniques and interpolation methods, we prove that the space–time decay rate of the k-th order spatial derivative ( \(0\le k \le N\) ) of the strong solution in the weighted Lebesgue space \( L_\gamma ^2 \) is \(t^{-\frac{3}{4}-\frac{k}{2}+\gamma }\) for any integer \(N\ge 3\) . The key contribution lies in developing a unified framework that connects weighted energy estimates with time decay analysis, enabling simultaneous capture of both spatial regularity and temporal decay characteristics. This result improves previous decay estimates and provides a complete description of the solution’s asymptotic behavior for the compressible Navier-Stokes equations with hyperbolic heat conduction.
