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On the Generalized Porous Medium Equation in Fourier-Besov Spaces |
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| Authors: | Weiliang Xiao & Xuhuan Zhou |
| Abstract: | We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions. |
| Keywords: | Porous medium equation well-posedness blowup criterion Fourier-Besov spaces |
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