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The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional case....
The incompressible Navier-Stokes problem is discretized in time by
the two-step backward differentiation formula.
Error estimates are proved under feasible assumptions on the
regularity of the exact solution avoiding hardly fulfillable
compatibility conditions. Whereas the time-weighted velocity error is
of optimal second order, the time-weighted error in the pressure is
of first order. Suboptimal estimates are shown for a
linearisation. The results cover both the two- and
three-dimensional...
In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.
We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space where is an invariant measure
We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
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