论文标题
托里的准线性汉密尔顿schrödinger方程的本地良好性
Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori
论文作者
论文摘要
我们证明了$ \ mathbb {t}^d $ in任何$ d \ geq 1 $ $ \ mathbb {t}^d $上的Quasi-Linearschrödinger方程的本地序列结果。对于Sobolev space $ h^s $的任何初始条件，$ s $大，我们证明了与等式相关的凯奇问题的经典解决方案的存在和独立性。这种解决方案的寿命仅取决于初始基准的大小。此外，我们证明了解决方案图的连续性。
We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger equations on $\mathbb{T}^d$ for any $d\geq 1$. For any initial condition in the Sobolev space $H^s$, with $s$ large, we prove the existence and unicity of classical solutions of the Cauchy problem associated to the equation. The lifespan of such a solution depends only on the size of the initial datum. Moreover we prove the continuity of the solution map.
