Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations
Journées équations aux dérivées partielles (1999), article no. 9, 11 p.

We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space B ˙ 2 n 2-2 p, (𝐑 n ), when the nonlinearity is of type u p , for p𝐍. This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.

@article{JEDP_1999____A9_0,
     author = {Planchon, Fabrice},
     title = {Self-similar solutions and {Besov} spaces for semi-linear {Schr\"odinger} and wave equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {9},
     publisher = {Universit\'e de Nantes},
     year = {1999},
     zbl = {01810582},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1999____A9_0/}
}
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Planchon, Fabrice. Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations. Journées équations aux dérivées partielles (1999), article  no. 9, 11 p. http://archive.numdam.org/item/JEDP_1999____A9_0/

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