Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
The author develops integral-equation techniques to obtain some results in the case of purely homogeneous-Dirichlet boundary conditions. The role of the thinness of the domain is replaced by the reciprocal of the first eigenvalue of the Laplacian. It is also shown the utility of the integral-equation techniques by bootstrapping global \(H^1\)-bounds, whenever available in 2D or 3D, into higher-order global bounds with slightly smoother forcing functions than those assumed by \textit{C. Guillopé} [Ann. Inst. Fourier 32, No. 3, 1-37 (1982; Zbl 0497.35075)], but otherwise more general, in that \(L^p\)-integrable singularities in time are allowed.
homogeneous-Dirichlet boundary conditions
scientific article; zbMATH DE number 885506