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| This is a joint work together with Lavi Karp in which we consider the
Einstein--Euler system in asymptotically flat spacetimes and therefore
use the condition that the energy density might vanish or tend to zero
at infinity, and that the pressure is a fractional power of the energy
density.
In this setting we prove local in time existence, uniqueness and
well-posedness of classical solutions.
The zero order term of our system contains an expression which might
not be a $C^?$ function and therefore causes an additional technical
difficulty.
In order to achieve our goals we use a certain type of weighted
Sobolev space of fractional order.
In a previous work we constructed an initial data set for these of
systems in the same type of weighted Sobolev spaces.
We obtain the same lower bound for the regularity as in the case of
the vacuum Einstein equations.
However, due to the presence of an equation of state with fractional
power, the regularity is bounded from above. |
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