Related papers: Stability of two-dimensional steady Euler flows wi…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
We prove the global uniqueness of multidimensional subsonic flows for the steady Euler--Poisson system in a bounded nozzle in the sense that uniqueness holds without restricting solutions to be small perturbations of a background state. The…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value…
This paper establishes the nonlinear stability of the Couette flow for the 2D Boussinesq equations with only vertical dissipation. The Boussinesq equations concerned here model buoyancy-driven fluids such as atmospheric and oceanographic…
The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal veloicty in the upstream, there exists a critical value…
In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.
In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli's function in the upstream is…
In this paper the dynamical stability of the Type IIA flow with no source near its stationary points is established. These stationary points had been shown previously by the authors to be Ricci-flat K\"ahler metrics on Calabi-Yau 3-folds.…
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and without swirl) which constitutes a desingularization of the…
In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler equations with compact support but non-concentrated around one or several points. Our solutions are of patch type, have analytic boundary,…
A new method for the creation of 3D solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations,…
This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions…
In this paper, we control the growth of the support of particular solutions to the Euler two-dimensional equations, whose vorticity is concentrated near special vortex crystals. These vortex crystals belong to the classical family of…
For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence…
In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow…
This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…
Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the…
We prove the existence of steady \emph{space quasi-periodic} stream functions, solutions for the Euler equation in vorticity-stream function formulation in the two dimensional channel ${\mathbb R}\times [-1,1]$. These solutions bifurcate…
For the 2D incompressible Euler equations, we establish global-in-time ($t \in \mathbb{R}$) stability of vortex quadrupoles satisfying odd symmetry with respect to both axes. Specifically, if the vorticity restricted to a quadrant is…