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• W3076753620 abstract "In this paper, we study a one dimensional nonlinear equation with diffusion $-nu(-partial_{xx})^{frac{alpha}{2}}$ for $0leq alphaleq 2$ and $nu>0$. We use a viscous-splitting algorithm to obtain global nonnegative weak solutions in space $L^1(mathbb{R})cap H^{1/2}(mathbb{R})$ when $0leqalphaleq 2$. For subcritical $1<alphaleq 2$ and critical case $alpha=1$, we obtain global existence and uniqueness of nonnegative spatial analytic solutions. We use a fractional bootstrap method to improve the regularity of mild solutions in Bessel potential spaces for subcritical case $1<alphaleq 2$. Then, we show that the solutions are spatial analytic and can be extended globally. For the critical case $alpha=1$, if the initial data $rho_0$ satisfies $-nu<infrho_0<0$, we use the characteristics methods for complex Burgers equation to obtain a unique spatial analytic solution to our target equation in some bounded time interval. If $rho_0geq0$, the solution exists globally and converges to steady state." @default.
• W3076753620 created "2020-08-24" @default.
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• W3076753620 date "2020-08-20" @default.
• W3076753620 modified "2023-10-16" @default.
• W3076753620 title "Global existence and spatial analyticity for a nonlocal flux with fractional diffusion" @default.
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• W3076753620 doi "https://doi.org/10.48550/arxiv.2008.08860" @default.
• W3076753620 hasPublicationYear "2020" @default.
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