Well posedness of the nonlinear Schrödinger equation with isolated singularities
نویسندگان
چکیده
We study the well posedness of nonlinear Schrödinger (NLS) equation with a point interaction and power nonlinearity in dimension two three. Behind autonomous interest problem, this is model evolution so called singular solutions that are known analysis semilinear elliptic equations. show Cauchy problem for NLS considered enjoys local existence uniqueness strong (operator domain) solutions, depend continuously from initial data. In holds any global proved powers below cubic. three restricted to low powers.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2021
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2021.10.017