Regularity Bounds on Zakharov System Evolutions

Smoothing and Global Attractors for the Zakharov System on the Torus

In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the difference of the nonlinear and the linear evolution is in a smoother space for all times the solution exists. The smoothing index depends on a parameter distinguishing the resonant and nonresonant cases...

Low Regularity Global Well-posedness for the Zakharov and Klein-gordon-schrödinger Systems

We prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schrödinger system, which are systems in two variables u : Rx × Rt → C and n : Rx × Rt → R. The Zakharov system is known to be locally well-posed in (u, n) ∈ L2×H−1/2 and the Klein-Gordon-Schrödinger system is known to be locally well-posed in (u, n) ∈ L × L. Here, we show that the Zakharov and Klein-Go...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

Regularity Properties of the Zakharov System on the Half Line

In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial...

A variational method to study the Zakharov equation

A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of ...