Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this pap...

In this paper, we introduce a general Bayesian approach to estimate polarization parameters in the Stokes imaging framework. We demonstrate that this new approach yields a neat solution to the polarimetric data reduction problem that preserves the physical admissibility constraints and provides a robust clustering of Stokes images in regard to image noises. The proposed approach is extensively ...

This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward selfsimilar solutions with finite total energy, which generalizes the results for the case of the isothermal compressible Navier-Stokes equations in Z. Guo and S. Jiang (Self-similar solutions to ...

We discuss well-posedness and convergence theory for the DPG method applied to a general system of linear Partial Differential Equations (PDEs) and specialize the results to the classical Stokes problem. The Stokes problem is an iconic troublemaker for standard Bubnov Galerkin methods; if discretizations are not carefully designed, they may exhibit non-convergence or locking. By contrast, DPG d...

Abstract. This paper discusses the symbol of the Hessian of a shape optimization problem in a viscid, incompressible flow. The symbol of the Hessian for the Stokes shape optimization problem is analytically approximated by tracking a Fourier mode through the operators involved. We propose a discrete method for finding the symbol and confirm the correctness by comparison with the analytical data...

The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions.

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differentia...

The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results p...