| Abstract: |
| We study the global existence of classical solutions to the Euler--Nordstrom system,
which incorporates a linear equation of state and a positive cosmological constant. The
system can be written as a coupled system of wave equations: a semilinear wave equation
for the Nordstrom gravitational field, whose source contains a fractional-power
nonlinearity; and an acoustical equation, which is a quasilinear wave equation with
nonlinearities involving first-order derivatives.
We restrict attention to spatially periodic perturbations of the background metric and
formulate the problem on the three-dimensional torus, working within the corresponding
Sobolev spaces. The emphasis is on the scalar gravitational field equation. We also
discuss related questions for the Euler--Poisson and Euler--Einstein systems.
This is joint work with U. Brauer (Universidad Complutense Madrid). |
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