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Global existence and asymptotic behavior for the full compressible Euler equations with damping in $\mathbb R^3$

Volume 119 / 2017

Guochun Wu, Zhensheng Gao Annales Polonici Mathematici 119 (2017), 147-163 MSC: Primary 76W05; Secondary 35Q35. DOI: 10.4064/ap4020-2-2017 Published online: 18 April 2017

Abstract

We are concerned with the global existence and asymptotic behavior of classical solutions to the Cauchy problem for the full compressible Euler equations with damping in $\mathbb R^3$. We prove the global existence of the classical solutions by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in $H^3$-framework. An energy estimate on $\| \nabla u\| _{L^1((0,t);\tilde{B}^{0,{3/2}}_{2,1}(\mathbb R^3))}$ enables us to close the energy estimates for the non-dissipative entropy. Moreover, the optimal time decay rate is also established.

Authors

  • Guochun WuSchool of Mathematical Sciences
    Huaqiao University
    Quanzhou 362021, China
    e-mail
  • Zhensheng GaoSchool of Mathematical Sciences
    Huaqiao University
    Quanzhou 362021, China
    e-mail

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