The Blowup Mechanism of Small Data Solutions for the Quasilinear Wave Equations in Three Space Dimensions |
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Authors: | Hui Cheng Yin |
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Affiliation: | (1) Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China, Institute of Mathematical Science, Chinese University of HongKong, Shatin, N. T., Hong Kong E-mail: huicheng@nju.edu.cn, CN |
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Abstract: | For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and Hörmander. As an application of our result, we show that the solution of three-dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac. |
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Keywords: | Lifespan Blowup system Nash-Moser method Commutator method |
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