Chemin et al. [M2AN Math. Model. Numer. Anal., 34 (2000), pp. 315–335.] considered the three-dimensional Navier–Stokes equations with vanishing vertical viscosity. Assuming that the initial velocity is square-integrable in the horizontal direction and Hs in the vertical direction, they prove existence of solutions for s > 1/2 and uniqueness of solutions for s > 3/2. Here, we close the gap betwe...

The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and suucient conditions are given in terms of the Jor-dan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Her...

Two uniqueness results for C0 semigroups on weighted Lp spaces over Rn generated by operators of type + r with singular drift are proven. A key ingredient in the proofs is the veri cation of some kind of \weak Kato inequality" which seems to break down exactly for those drift singularities where Lp uniqueness breaks down as well. 3 Lp uniqueness of non{symmetric di usion operators with singular...

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell equations on an admissible Riemannian manifold, and a uniqueness result for Maxwell equations in Euclidean space with admissible matrix coefficients. The proo...

In this paper we will give a new proof by using group action to prove the uniqueness of maximal Sperner familiesFmax of [n].We will also prove the uniqueness of Sperner familiesF of [n]with |F|= ( n n2 ) −1 by using a combinatorial approach. Furthermore, by using the uniqueness of Sperner family, we will classify all the structures of (1, 2) superimposed codes of size 9× 10 and 9× 11. © 2006 El...