Shunya Hashimoto

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math.AP2024

The well-posedness of the stochastic nonlinear SchrÃ¶dinger equations in $H^{2} (R^{d})$

Isamu DÃ´ku, Shunya Hashimoto, Shuji Machihara

The Cauchy problem for the stochastic nonlinear SchrÃ¶dinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients a…

math.AP2024

Global solution for the stochastic nonlinear SchrÃ¶dinger system with quadratic interaction in four dimensions

Masaru Hamano, Shunya Hashimoto, Shuji Machihara

We discuss the global existence of solutions to a system of stochastic SchrÃ¶dinger equations with multiplicative noise. Our setting of the quadratic nonlinear terms in dimension 4…

The well-posedness of the stochastic nonlinear SchrÃ¶dinger equations in H2(Rd)

Global solution for the stochastic nonlinear SchrÃ¶dinger system with quadratic interaction in four dimensions

The well-posedness of the stochastic nonlinear SchrÃ¶dinger equations in $H^{2} (R^{d})$