Global smooth solutions for a non-linear system of wave equations

Existence, blow-up, and exponential decay estimates for a system of nonlinear wave equations with nonlinear boundary conditions

“…Problems of this type arise in material science and physics, which have been studied by many authors. For example, we refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references given therein. In these works, many interesting results about the existence, regularity, and the asymptotic behavior of solutions were obtained.…”

Low regularity for the nonlinear Klein–Gordon systems

“…In [9] Miao, Zhang and Fang answered the problem of global well-posedness for the Klein-Gordon equation below the energy norm by means of Bourgain's method [1]. For many results in wave system and Klein-Gordon system, see [6][7][8]. We intend to get a similar result on the defocusing Klein-Gordon system using a different method, inspired by Isabelle Gallagher and Fabrice Planchon [11].…”

Scattering theory for a nonlinear system of wave equations with critical growth

“…In this note, we continue our study from [3,4] on the following nonlinear system of wave equations with Hamilton structure:…”

“…To ensure that the potential energy of problem (1.1) tends to zero as t → ∞, which will play an important role in the proof of our result, we need to assume that F, F 1 , F 2 satisfy the following assumptions similar to those in [3,4]…”

“…the function F (|u| 2 , |v| 2 ) = |u| 6 + |u| 4 |v| 2 + |u| 2 |v| 4 + |v| 6 satisfies (H1)-(H5) in the space dimension n = 3. For the physical background and related research on the wave equation, we refer the reader to [1,[3][4][5][6][7] and the references therein. Let us end this section by recalling what we have done in our previous papers.…”