On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain

Yoshihiro Shibata

doi:10.3934/cpaa.2018081

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2018, Volume 17, Issue 4: 1681-1721. Doi: 10.3934/cpaa.2018081

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On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain

Yoshihiro Shibata^1,2,

1.
Department of Mathematics and Reseach Institute of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan
2.
Deparment of Mechanical Engineering and Materials Science University of Pittsburgh, USA

Received: February 2017

Revised: July 2017

Published: April 2018

Partially supported by JSPS@Grant-in-aid for Scientific Research (A) -17H0109, Top Global University Project, and JSPS program of the Japanese-German Graduate Externship.

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This paper deals with the local well-posedness of free boundary problems for the Navier-Stokes equations in the case where the fluid initially occupies an exterior domain $Ω$ in $N$ -dimensional Euclidian space $\mathbb{R}^N$ .

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D07.

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References

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