相关论文: Construction of Maximal Functions associated with …

A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…

Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010…

We consider an incompressible fluid in a three-dimensional pipe, following the Navier-Stokes system with classical boundary conditions. We are interested in the following question: is there any optimal shape for the criterion "energy…

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes…

Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…

Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…

In this paper, we construct a new class of blowup solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. In detail, we obtain a class of global rotational exact solutions…

We prove the existence of solutions for the axisymmetric steady Navier-Stokes system around an infinite cylinder under external forces. The solutions are constructed to be decaying at the horizontal infinity, despite an analogue of the…

Higher-order estimates in weighted Sobolev spaces for solutions to a singular elliptic equation for the stream function in an axially symmetric cylinder are provided. These estimates are essential for investigating the existence of axially…

We introduce the new concept of maximal dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumption, we show that maximal dissipative solutions are well posed as long as the bigger class of dissipative…

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of…

This investigation concerns a systematic search for potentially singular behavior in 3D Navier-Stokes flows. Enstrophy serves as a convenient indicator of the regularity of solutions to the Navier Stokes system --- as long as this quantity…

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…

In the context of some bidimensionnal Navier-Stokes model, we exhibit a family of exact oscillating solutions $\{u_{\epsilon}\}_{\epsilon}$ defined on some strip $[0,T]\times\R^2$ which does not depend on $\epsilon\in]0,1]$. The exact…

This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity of solutions to the Navier-Stokes equations, hypercomplex…

We consider the setting of manifolds with ends which are obtained by compact perturbation (gluing) of ends of the form $\mathbb{R}^{n_i}\times \mathcal{M}_i$. We investigate family of vertical resolvent…

In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids,…

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

We investigate a compressible two-fluid Navier-Stokes type system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. We are…

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…