相关论文: Rigidity of singularities of 2D gravity water wave…

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate…

We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow $U(x_2)$, $x_2 \in (-h, 0)$, where the wave numbers $k$ of the horizontal variable $x_1$ is treated as a parameter. Our main…

In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…

This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two…

We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…

This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…

For the Cauchy problem of nonlinear elastic wave equations of three dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of classical solutions with small initial data was proved in…

In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow…

This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting…

We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of…

We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform…

The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…

In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows…

In this work we investigate the helicity regularity for weak solutions of the incompressible Euler equations. To prove regularity and conservation of the helicity we will threat the velocity $u$ and its $curl\, u$ as two independent…

We study weak solutions of the two-dimensional (2D) filtered Euler equations whose vorticity is a finite Radon measure and velocity has locally finite kinetic energy, which is called the vortex sheet solution. The filtered Euler equations…

This paper studies the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler…

This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface…

We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradiferential reduction established in the companion paper, we prove Strichartz estimates for solutions to this problem, at a…

We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…

We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new transport equations for vorticity, which both play a…