Article Contents
Article Contents

# Well-posedness for degenerate Schrödinger equations

• We consider the initial value problem for Schrödinger type equations $$\frac{1}{i}\partial_tu-a(t)\Delta_xu+\sum_{j=1}^nb_j(t,x)\partial_{x_j}u=0$$ with $a(t)$ vanishing of finite order at $t=0$ proving the well-posedness in Sobolev and Gevrey spaces according to the behavior of the real parts $\Re b_j(t,x)$ as $t\to0$ and $|x|\to\infty$. Moreover, we discuss the application of our approach to the case of a general degeneracy.
Mathematics Subject Classification: Primary: 35J10; Secondary: 35Q41.

 Citation:

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