Self-similar solutions and semi-linear wave equations in Besov spaces

By F. Planchon. 2000

47 citations recorded by the source corpus.

Abstract We prove that the initial value problem for semi-linear wave equations is well-posed in the Besov space B s p ,∞ 2 ( R n ) , where the nonlinearity is of type u p , with p∈ N and s p = n 2 − 2 p > 1 2 . This allows to obtain self-similar solutions as well as to recover previous results under weaker smallness assumptions on the data.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b597680ee8185fcd0b916eca9d67968e246c76c5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Luc Molinet
2. Francis Ribaud
3. Isabelle Gallagher
4. F. Planchon
5. Didier Pilod
6. Carlos E. Kenig
7. Baoxiang Wang
8. Nader Masmoudi

In Control and Systems Engineering

1. Luc Molinet
2. Francis Ribaud
3. F. Planchon
4. Isabelle Gallagher
5. Nicolas Burq
6. Dongho Chae
7. Didier Pilod

In Mathematical Physics

1. Luc Molinet
2. Francis Ribaud
3. F. Planchon
4. Isabelle Gallagher
5. Didier Pilod
6. Carlos E. Kenig
7. Baoxiang Wang
8. Nader Masmoudi

Citations in the corpus

• On the Cauchy Problem for the Generalized Korteweg-de Vries Equation (2003, methodology): “To conclude note that similar results have been obtained in Bourgain (1998) and Planchon (2002) for the critical 2D nonlinear Schr€odinger equation i@tuþ uþ juj2u ¼ 0 (we refer also to Planchon (2000) concerning the semi-linear wave equation).”
• On global solutions to a defocusing semi-linear wave equation (2003, background): “Note that one may even lower assumptions on γ to γ > 0, as any positive smoothness can be propagated (see [16], [15]).”