Abstract
AbstractIn the paper the global motion of a viscous compressible heat conducting capillary fluid in a domain bounded by a free surface is considered. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global‐in‐time solution which is close to the constant state for any moment of time. The solution is obtained in such Sobolev–Slobodetskii spaces that the velocity, the temperature and the density of the fluid have $W_2^{2+\alpha,1+\alpha/2}$\nopagenumbers\end, $W_2^{2+\alpha,1+\alpha/2}$\nopagenumbers\end and $W_2^{1+\alpha,1/2+\alpha/2}$\nopagenumbers\end —regularity with α∈(¾, 1), respectively. Copyright © 2001 John Wiley & Sons, Ltd.
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