2016/04/17 by Young-Pil Choi, Choi, Young-Pil, Bongsuk Kwon +1 · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1604.04886
openalex publication_date 2016/04/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We present a new hydrodynamic model consisting of the pressureless Euler\nequations and the isentropic compressible Navier-Stokes equations where the\ncoupling of two systems is through the drag force. This coupled system can be\nderived, in the hydrodynamic limit, from the particle-fluid equations that are\nfrequently used to study the medical sprays, aerosols and sedimentation\nproblems. For the proposed system, we first construct the local-in-time\nclassical solutions in an appropriate L2 Sobolev space. We also establish\nthe \a priori large-time behavior estimate by constructing a Lyapunov\nfunctional measuring the fluctuation of momentum and mass from the averaged\nquantities, and using this together with the bootstrapping argument, we obtain\nthe global classical solution. The large-time behavior estimate asserts that\nthe velocity functions of the pressureless Euler and the compressible\nNavier-Stokes equations are aligned exponentially fast as time tends to\ninfinity.\n