15 research outputs found
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation
We consider the Neumann type problem of the heat equation in a moving thin
domain around a given closed moving hypersurface. The main result of this paper
is an error estimate in the sup-norm for classical solutions to the thin domain
problem and a limit equation on the moving hypersurface which appears in the
thin-film limit of the heat equation. To prove the error estimate, we show a
uniform a priori estimate for a classical solution to the thin domain problem
based on the maximum principle. Moreover, we construct a suitable approximate
solution to the thin domain problem from a classical solution to the limit
equation based on an asymptotic expansion of the thin domain problem and apply
the uniform a priori estimate to the difference of the approximate solution and
a classical solution to the thin domain problem.Comment: 27 page
ON ANALYTICITY OF THE -STOKES SEMIGROUP FOR SOME NON-HELMHOLTZ DOMAINS
Consider the Stokes equations in a sector-like C3 domain Ω R2. It is shown that the Stokes operator generates an analytic semigroup in Lp (Ω) for p 2 [2;1). This includes domains where the Lp-Helmholtz decomposition fails to hold. To show our result we interpolate results of the Stokes semigroup in VMO and L2 by constructing a suitable non-Helmholtz projection to solenoidal spaces