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Expanding large global solutions of the equations of compressible fluid mechanics

  • Mahir Hadžić
  • Juhi Jang
Article

Abstract

Without any symmetry assumptions on the initial data we construct global-in-time unique solutions to the vacuum free boundary three-dimensional isentropic compressible Euler equations when the adiabatic exponent \(\gamma \) lies in the interval \((1,\frac{5}{3}]\). Our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by Sideris and they satisfy the physical vacuum boundary condition.

Notes

Acknowledgements

The authors express their gratitude to P. Raphaël for fruitful discussions and for pointing out connections to the treatment of self-similar singular behavior for nonlinear Schrödinger equations. They also thank C. Dafermos for his feedback and pointing out important references. JJ is supported in part by NSF Grants DMS-1608492 and DMS-1608494 and a von Neumann fellowship of the Institute for Advanced Study through the NSF grant DMS-1128155. MH acknowledges the support of the EPSRC Grant EP/N016777/1.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonStrand, LondonUK
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Korea Institute for Advanced StudySeoulKorea

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