Related papers: Sharp Strong Convergence in Ideal Flows

In this paper, we study the uniformly rotating vortex patch solutions for the 2D incompressible Euler equations. Specifically, we prove that if the patch solution is close to the Rankine vortex in a certain weak topology, it is either the…

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also…

In this paper, we first present a new and simple proof of unboundedness of Riesz operator in $L^\infty$ and then establish the mild ill-posedness in $W^{1,\infty}$ of 3D rotating Euler equations and 2D Euler equations with partial damping.…

We study the large-time behavior of finite-energy weak solutions for the Vlasov-Navier-Stokes equations in a two-dimensional torus. We focus first on the homogeneous case where the ambient (incompressible and viscous) fluid carrying the…

We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions were introduced as a generalized solution framework in…

This paper extends the mathematical theory of axisymmetrization and vorticity depletion within the two-dimensional (2D) Euler equations, with an emphasis on the dynamics of radially symmetric, monotonic vorticity profiles. By analyzing…

We prove that any sequence of vanishing viscosity Leray-Hopf solutions to the periodic two-dimensional incompressible Navier-Stokes equations does not display anomalous dissipation if the initial vorticity is a measure with positive…

We study the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations (CNS) under general pressure laws in all dimensions $d\geq 2$. For all hypo-viscosities $(-\Delta)^\alpha$ with $\alpha\in (0,1)$, we prove…

In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in…

We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…

It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…

In this paper, we obtain sharp Strichartz estimates for solutions of the wave equation $\square_\gg\phi=0$ where $\gg$ is a rough Lorentzian metric on a 4 dimensional space-time $\MM$. This is the last step of the proof of the bounded $L^2$…

We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…

In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs to $L^1_{\rm loc}([0,+\infty);L^{\rm…

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary…

In this paper, we mainly investigate the tridimensional incompressible axisymmetric Euler equations without swirl in the whole space. Specifically, we prove the global existence of weak solutions if the swirl component of initial vorticity…

We are concerned with global weak solutions to the isentropic compressible Euler equations with cylindrically symmetric rotating structure, in which the origin is included. Due to the presence of the singularity at the origin, only the case…

This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…

We are concerned with the existence and compactness of entropy solutions of the compressible Euler system for two-dimensional steady potential flow around an obstacle for a polytropic gas with supersonic far-field velocity. The existence…

We investigate the existence of stationary and traveling wave solutions to the 2D Euler equations near the Couette flow in the infinite channel $\mathbb{R} \times [-1,1]$. For Sobolev spaces $W^{s,p}$ or H\"older spaces $C^s$, we identify…