Related papers: Non-Uniqueness in Plane Fluid Flows
This article is devoted to stationary solutions of Euler's equation on a rotating sphere, and to their relevance to the dynamics of stratospheric flows in the atmosphere of the outer planets of our solar system and in polar regions of the…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems,…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…
Due to the highly degeneracy and singularities of the entropy equation, the physical entropy for viscous and heat conductive polytropic gases behave singularly in the presence of vacuum and it is thus a challenge to study its dynamics. It…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles…
Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a velocity field computed through a self-consistent…
We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The…
We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…
We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…
Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with {\sl physical} viscosity and capillarity effects…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
We use guiding principles from nonequilibrium thermodynamics to develop an admissible set of 13 moment equations for rarefied gas flows. The main benefits of our thermodynamic approach are an explicit entropy expression fulfilling an $H$…
In this paper, we establish an $\epsilon$-regularity criterion for any weak solution $(u,d)$ to the nematic liquid crystal flow (1.1) such that $(u,\nabla d)\in L^p_tL^q_x$ for some $p\ge 2$ and $q\ge n$ satisfying the condition (1.2). As…
We address the question whether a singularity in a three-dimensional incompressible inviscid fluid flow can occur in finite time. Analytical considerations and numerical simulations suggest high-symmetry flows being a promising candidate…