Existence and uniqueness of global solutions of nonlinear Schrödinger equations on \(\mathbb{R}^ 2\). (English) Zbl 0887.35141
Summary: We consider the solutions of the nonlinear Schrödinger equations
\[
{\partial u\over\partial t}- i\Delta u+|u|^pu= f,\quad u(x,0)= u_0(x),
\]
where \(u\) is defined on \(\mathbb{R}^+\times \mathbb{R}^2\). We prove the existence and uniqueness of global weak solutions of the above equations. Lastly, we consider the special case: \(p=2\), and we obtain the strong solutions.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
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