Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions |
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Authors: | Li Jun Yin Huicheng |
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Institution: | 1. Department of Mathematics and IMS, Nanjing University, Nanjing 210093, P.R. China;2. School of Mathematical Sciences and Institute of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. China |
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Abstract: | The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude. |
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Keywords: | 35L10 35L71 35L05 Quasilinear wave equation Exterior domain Neumann boundary condition Null condition Convex obstacle Elliptic regularity |
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