Related papers: Statistical solutions of the incompressible Euler …
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
In this article, we study the 2D incompressible steady Navier-Stokes equation in a channel $(-L,0)\times(-1,1)$ with the no-slip boundary condition on $\{Y = \pm 1\}$, and consider the inviscid limit $\varepsilon \to 0$. In the special case…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
We construct a class of spatially polynomial velocity fields that are exact solutions of the planar unsteady Navier-Stokes equation. These solutions can be used as simple benchmarks for testing numerical methods or verifying the feasibility…
In this note, we study the random data problem for incompressible Navier-Stokes equations in Euclidean space with arbitrary regularity, using the randomization introduced in \cite{Shen-Soffer-Wu-2021-1}.
Based on the essential connection of the parabolic inertia Lam\'{e} equations and Navier-Stokes equations, we prove the existence of smooth solutions of the incompressible Navier-Stokes equations in three-dimensional Euclidean space…
We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that,…
The present paper is dedicated to the global large solutions and incompressible limit for the compressible Navier-Stokes system in $\mathbb{R}^d$ with $d\ge 2$. We aim at extending the work by Danchin and Mucha (Adv. Math., 320, 904--925,…
The Navier-Stokes equations describing laminar flow of an incompressible fluid will be solved. Different group of general solutions for Navier stokes equations governing Laminar incompressible fluids will be derived.
We consider the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d; the quadratic term in these equations arises from the bilinear map sending two velocity fields v, w : T^d -> R^d into v . D w, and also…
The stationary version of a modified definition of statistical solution for the three-dimensional incompressible Navier-Stokes equations introduced in a previous work is investigated. Particular types of such stationary statistical…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
A detailed study of complex-space singularities of the two-dimensional incompressible Euler equation is performed in the short-time asymptotic r\'egime when such singularities are very far from the real domain; this allows an exact…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
We establish the local existence and uniqueness of solutions to the two-dimensional compressible Euler equations with initial velocity $\bv_0$, logarithmic density $\rho_0$, and specific vorticity \(w_0\), which satisfy $(\bv_0, \rho_0,…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes equations with…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…
In this paper, we study permutation symmetric solutions of the incompressible Euler equation. We show that the dynamics of these solutions can be reduced to an evolution equation on a single vorticity component $\omega_1$, and we…