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Abstract:
In this paper, we consider the large time behavior of planar shock wave for 3D compressible isentropic Navier-Stokes equations (CNS) in half space. Providing the strength of the shock wave and initial perturbations are small, we proved the planar shock wave for 3D CNS is nonlinearly stable in half space with Navier boundary condition. The main difficulty comes from the compressibility of shock wave, which leads to lower order terms with bad sign, see the third line in (4.36). We apply a decomposition of the solution into zero and non-zero modes: we take the anti-derivative for the zero mode and obtain the space-time estimates for the energy of perturbation itself. Then combining the fact that the Poincar & eacute; inequality is available for the non-zero mode, we have successfully controlled the lower order terms with bad sign in (4.36). To overcome the difficulty that comes from the boundary, we introduce the two crucial estimates on boundary lemma (4.2) and fully utilize the property of Navier boundary conditions, which means that the normal velocity is zero on the boundary and the fluid tangential velocity is proportional to the tangential component of the viscous stress tensor on the boundary. Finally, the nonlinear stability is proved by the weighted energy method.
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Source :
NONLINEARITY
ISSN: 0951-7715
Year: 2025
Issue: 3
Volume: 38
1 . 7 0 0
JCR@2022
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ESI Highly Cited Papers on the List: 0 Unfold All
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Chinese Cited Count:
30 Days PV: 20
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