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Expanding large global solutions of the compressible Euler equations

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NWW - Nonlinear water waves

In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the free boundary compressible Euler equations satisfying the physical vacuum condition.  The support of these solutions expands at a linear rate in time. We show that if the adiabatic exponent gamma belongs to the interval(1, 5/3] then these affine motions are globally-in-time nonlinearly stable.



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