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math.AP2020
Necessary and sufficient condition for global existence of solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity
Kazumasa Fujiwara, Vladimir Georgiev
We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-e…
math.AP2020★ 6 cited
A test function method for evolution equations with fractional powers of the Laplace operator
Kazumasa Fujiwara, Marcello D'Abbicco
In this paper, we discuss a test function method to obtain nonexistence of global-in-time solutions for higher order evolution equations with fractional derivatives and a power non…
math.AP2020
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in…