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Pointwise wave behavior of the Navier-Stokes equations in half space

Du is supported by NSFC(Grant No. 11526049 and 11671075) and the Fundamental Research Funds for the Central Universities (No. 2232016D-22)

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  • In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound speed in two opposite directions and reflected heat kernel (due to the boundary effect) propagating with positive sound speed. With the strong wave interactions, the nonlinear analysis exhibits the rich wave structure: the diffusion waves interact with each other and consequently, the solution decays with algebraic rate.

    Mathematics Subject Classification: 76N10, 35B40, 35A08.


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  •   S. J. Deng , W. K. Wang  and  S.-H. Yu , Green's functions of wave equations in $R^n_+ × R_+$, Arch. Ration. Mech. Anal., 216 (2015) , 881-903.  doi: 10.1007/s00205-014-0821-2.
      S. J. Deng , Initial-boundary value problem for p-system with damping in half space, Nonlinear Analysis, 143 (2016) , 193-210.  doi: 10.1016/j.na.2016.05.009.
      S. J. Deng  and  S.-H. Yu , Green's function and pointwise convergence for compressible Navier-Stokes equations, Quart. Appl. Math., 75 (2017) , 433-503.  doi: 10.1090/qam/1461.
      L. L. Du , Characteristic half space problem for the Broadwell model, Netw. Heterog. Media, 9 (2014) , 97-110.  doi: 10.3934/nhm.2014.9.97.
      L. L. Du and Z. G. Wu, Solving the non-isentropic Navier-Stokes equations in Odd Space Dimensions: the Green Function Method, J. Math. Phys., 58 (2017), 101506, 38 pp.
      C.-Y. Lan , H.-E. Lin  and  S.-H. Yu , The Green's function for the Broadwell model with a transonic boundary, J. Hyperbolic Differ. Equ., 5 (2008) , 279-294.  doi: 10.1142/S0219891608001489.
      T.-P. Liu  and  S.-H. Yu , Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation, Comm. Pure Appl. Math., 60 (2007) , 295-356.  doi: 10.1002/cpa.20172.
      T. -P. Liu and Y. N. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc. Mem. Amer. Math. Soc. , 125 (1997), ⅷ+120 pp.
      T.-P. Liu  and  Y. N. Zeng , Compressible Navier-Stokes equations with zero heat conductivity, J. Differential Equations, 153 (1999) , 225-291.  doi: 10.1006/jdeq.1998.3554.
      A. Matsumura  and  T. Nishida , Initial boundary value problem for the equations of motion of compressible viscous and heat conductive fluids, Comm. Math. Phys., 89 (1983) , 445-464. 
      Y. Kagei  and  T. Kobayashi , On large time behavior of solutions to the Compressible Navier-Stokes Equations in the half space in $R^3$, Arch. Ration. Mech. Anal., 165 (2002) , 89-159.  doi: 10.1007/s00205-002-0221-x.
      Y. Kagei  and  T. Kobayashi , Asymptotic behavior of solutions of the compressible Navier-Stokes equations on the half space, Arch. Ration. Mech. Anal., 177 (2005) , 231-330.  doi: 10.1007/s00205-005-0365-6.
      H. T. Wang  and  S.-H. Yu , Algebraic-complex scheme for Dirichlet-Neumann data for parabolic system, Arch. Ration. Mech. Anal., 211 (2014) , 1013-1026.  doi: 10.1007/s00205-013-0699-4.
      Y. Zeng , $L^1$ asymptotic behavior of compressible, isentropic, viscous 1-D flow, Comm. Pure Appl. Math., 47 (1994) , 1053-1082.  doi: 10.1002/cpa.3160470804.
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