We present new extended Strichartz estimates for the solutions to the heat equation with inhomogeneous nonlinearity in the mass-energy intercritical framework in space dimension d ≥ 1. As an application we show local and global well-posedness in the Strichartz space L~q((0,T); L~r(R~d)), both in the focusing and the defocusing case, assuming the initial data are in the Sobolev space H~σ(R~d)), with σ ∈ (0, 1].
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机译：我们为Quality-enertional临界框架中具有不均匀非线性的热方程的解决方案提供了新的扩展Strichartz估计，在空间尺寸D≥1中。作为我们在Strichartz Space L〜Q中显示出本地和全球良好的良好的应用（（ 0，t）; L〜R（r〜d）），既在聚焦和散焦外壳中，假设初始数据都处于SoboLev Space H〜σ（R〜D）），具有σ∈（0,1 ]。
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