In this paper, we study the zero dissipation limit problem for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids. We prove that if the solution of the inviscid Euler equations is piecewise smooth with finitely many noninteracting shocks satisfying the entropy condition, then there exist solutions to Navier-Stokes equations which converge to the inviscid solution away from shock discontinuities at a rate of $\epsilon^1$ as the viscosity $\epsilon$ tend to zero, provided that the heat-conducting coefficient $k = 0($\epsilon$).

It will be shown that the Reeh-Schlieder property holds for states of quantum fields for ultrahyperfunctional Wightman theory. As by product, it is shown that the Reeh-Schlieder property also holds for states of quantum fields on a non-commutative Minkowski space in the setting ultrahyperfunctional.

The aim of this paper is to prove existence of non negative compactly supported solutions for a nonlinear degenerate parabolic equation with a non Lipschitz source term in one space dimension. This equation mimics the properties of the classical $k-\epsilon$ model in the context of turbulent mixing flows with respect to nonlinearities and support properties of solutions.

To the authors’ knowledge, originality of the method relies both in the fact with dealing with a non Lipschitz source term and in the comparison of not only the speed but also the acceleration of the support boundaries.

In this paper we analyze the behavior of Verblunsky parameters for Hermitian linear functionals deduced from canonical linear spectral transformations of a quasi-definite Hermitian linear functional. Some illustrative examples are studied.

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant scalar curvature. The proofs rely on barriers construction and a priori estimates.

We study the Schrödinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. This model has been proposed in [12]. Our primary interest here is in the boundary conditions successively in a half-plane, then in a quadrant of $\bbfR^2$. The half-plane problem has been used in [11] to build a numerical method, which has been introduced in the HERA plateform of CEA.