相关论文: A paradifferential reduction for the gravity-capil…

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…

It has recently been shown via an equivalence of gravitational radius and Compton wavelength in four dimensions that the trans-Planckian regime of gravity may by semi-classical, and that this point is defined by a minimum horizon radius…

The present paper is devoted to the study of the well-posedness and the lower bound of blow-up rate to the Cauchy problem of the generalized Zakharov(GZ) equations with magnetic field in R^d. The work of well-posedness of the GZ system…

The scattering of surface waves by structures intersecting liquid surfaces is fundamental in fluid mechanics, with prior studies exploring gravity, capillary, and capillary-gravity wave interactions. This paper develops a semi-analytical…

Capillary waves are perhaps the simplest example to consider for an introduction to wave turbulence. Since the first paper by Zakharov and Filonenko (1967), capillary wave turbulence has been the subject of many studies but a didactic…

A novel method is developed for extending the Green-Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation…

We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…

In the paper, we consider the Cauchy problem on the spatially one-dimensional Vlasov-Poisson-Landau system modelling the motion of ions under a generalized Boltzmann relation. Let the Knudsen number and the Debye length be given as…

We prove via explicitly constructed initial data that solutions to the gravity-capillary wave system in $\mathbb{R}^3$ representing a 2d air-water interface immediately fails to be $C^3$ with respect to the initial data if the initial data…

Nowadays we have many methods allowing to exploit the regularising properties of the linear part of a nonlinear dispersive equation (such as the KdV equation, the nonlinear wave or the nonlinear Schroedinger equations) in order to prove…

We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us…

We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…

The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the…

This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of…

Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…

This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the…

We give a new proof of Brakke's partial regularity theorem up to C^{1,\varsigma} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The…

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up to degree four. This proves a conjecture of…

In this article, we develop the local Cauchy theory for the gravity water waves system, for rough initial data which do not decay at infinity. We work in the context of $L^2$-based uniformly local Sobolev spaces introduced by Kato. We prove…

We study the dynamics of the collision of two solitary waves for the Zakharov-Kuznetsov equation in dimension $2$ and $3$. We describe the evolution of the solution behaving as a sum of $2$-solitary waves of nearly equal speeds at time…