Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in \re^3 via Solenoidal Hermite Polynomials

Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials. Extensions to well-posed Burnett equations with the bi-harmonic viscosity operator are also discussed.Comment: 16 pages. arXiv admin note: text overlap with arXiv:0901.428

On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials

An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials. Extensions to other linear and nonlinear singular PDEs are discussed.Comment: 22 page