No abstract

We proved L q − L ∞ type estimates of the Stokes semigroup in a 2-dimensional exterior domain. Our proof is based on the investigation of the asymptotic behavior of the resolvent of the Stokes operator near the origin.

Communicated by Y. ShibataWe prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non-linear thermoelastic equation as an important physical example.

We prove the unique existence of solutions to some mixed problem of hyperbolic parabolic coupled systems with Neumann boundary condition, and we investigate how the constant in the first energy estimate depends on the coefficients of the opertors.

No abstract