We formulate some conditions when non-uniqueness of approximate solutions of the stationary Navier-Stokes equations occurs. Introduction. In this paper we will be concerned with the stationary Navier-Stokes equations for incompressible liquid in a bounded domain in Rn (n ∈ {2, 3}). Since a long time, it has been known that there exists a weak solution of this problem. For example, general exist...

A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, " Note on the uniqueness of the solution of an equation of interest in inverse scattering problem " ,

Abstract We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established.

In this paper we propose a new notion of Forward-Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the backward stochastic differential equations. The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of a forward-backward stochastic differential equation (FBSDE...

A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, Note on the uniqueness of the solution of an equation of interest in inverse scattering problem,

In this paper, we prove the global uniqueness of determining both the magnetic field and the electrical potential by boundary measurements in two-dimensional case. In other words, we prove the uniqueness of this inverse problem without any smallness assumption.