Publication

Global dynamics of the nonradial energy-critical wave equation above the ground state energy

Joachim Krieger
2013
Journal Articles

Abstract

In this paper we establish the existence of certain classes of solutions to the energy critical nonlinear wave equation in dimensions 3 and 5 assuming that the energy exceeds the ground state energy only by a small amount. No radial assumption is made. We find that there exist four sets in H(over dot) x L-2 with nonempty interiors which correspond to all possible combinations of finite-time blowup on the one hand, and global existence and scattering to a free wave, on the other hand, as t -> +/-infinity.

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https://infoscience.epfl.ch/entities/publication/bdbed985-8e75-4200-976c-bf45d653a192

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Joachim Krieger
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/bdbed985-8e75-4200-976c-bf45d653a192

About this result

Related concepts (21)

Ground state

The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states.

Stokes wave

In fluid dynamics, a Stokes wave is a nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion. Stokes's wave theory is of direct practical use for waves on intermediate and deep water. It is used in the design of coastal and offshore structures, in order to determine the wave kinematics (free surface elevation and flow velocities).

Trochoidal wave

In fluid dynamics, a trochoidal wave or Gerstner wave is an exact solution of the Euler equations for periodic surface gravity waves. It describes a progressive wave of permanent form on the surface of an incompressible fluid of infinite depth. The free surface of this wave solution is an inverted (upside-down) trochoid – with sharper crests and flat troughs. This wave solution was discovered by Gerstner in 1802, and rediscovered independently by Rankine in 1863.

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