Related papers: Energy of tsunami waves generated by bottom motion

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the…

In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such…

In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the…

Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…

Collisionless shock waves are one of the main forms of energy conversion in space plasmas. They can directly or indirectly drive other universal plasma processes such as magnetic reconnection, turbulence, particle acceleration and wave…

Earthquakes are indeed triggered by fault dislocations, but whether this process alone can produce the actual earthquake energy released by the mainshock has long been questioned. Therefore, exploring the true source of energy that causes…

We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency $\w$, in the…

Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…

We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface…

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that…

The purpose of this article is to clarify the Cauchy theory of the water waves equations as well in terms of regularity indexes for the initial conditions as for the smoothness of the bottom of the domain (namely no regularity assumption is…

Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…

The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…

Shock wave theory was first studied for gas dynamics, for which shocks appear as compression waves. A shock wave is characterized as a sharp transition, even discontinuity in the flow. In fact, shocks appear in many different physical…

We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps which continuously injects velocity fluctuations…

In this paper we study the behaviors of the the energy of solutions of coupled wave equations on a compact manifold with boundary in the case of indirect nonlinear damping . Only one of the two equations is directly damped by a localized…

To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…

The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…

We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…

We obtain a general solution for the water waves resulting from a general, time-dependent surface pressure distribution, in the presence of a shear current of uniform vorticity beneath the surface, in three dimensions. Linearized governing…