Eigenvalue Asymptotics in Non-isothermal Elongational Flow

We shall furnish an asymptotic description of the spectrum of a C0-semigroup generator arising in non-isothermal elongational flow. It will be shown that the spectrum coincides asymptotically with isolated eigenvalues lined up along a logarithmic curve. The strategy for this result is based on delicate asymptotic estimates and ideas developed for the isothermal regime. These estimates can be successfully employed only since the spectral mapping theorem is valid for the semigroup.