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- W2247484641 abstract "We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation, $$ partial_t u + (-Delta)^{ 1/2} u = |nabla u|^p, quad x in mathbb R^N, t > 0, qquad u(x,0) = u_0(x) , quad x in mathbb R^N, $$ where $p > 1$ and $u_0 in B^1_{r,1}(mathbb R^N) cap B^1_{infty,1} (mathbb R^N)$ with $r in [1,infty]$. We show that for sufficiently small $u_0 in dot B^1_{infty,1}(mathbb R^N)$, there exists a global-in-time mild solution. Furthermore, we prove that the solution behaves asymptotically like suitable multiplies of the Poisson kernel." @default.
- W2247484641 created "2016-06-24" @default.
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- W2247484641 date "2015-09-18" @default.
- W2247484641 modified "2023-10-16" @default.
- W2247484641 title "Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces" @default.
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- W2247484641 doi "https://doi.org/10.48550/arxiv.1509.05540" @default.
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