Blow up and regularity for fractal Burgers equation
Blow up and regularity for fractal Burgers equation
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DOI：
10.4310/dpde.2008.v5.n3.a2
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发表时间：
2008-04
期刊：
影响因子：
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通讯作者：
A. Kiselev;F. Nazarov;R. Shterenberg
中科院分区：
文献类型：
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作者：
A. Kiselev;F. Nazarov;R. Shterenberg
本文研究了分数阶耗散Burgers方程解的存在性、唯一性、爆破性和正则性。我们证明了Laplacian $\alpha < 1/2，$的幂的有限时间爆破的存在性和$\alpha \geq 1/2的解的整体存在性和解析性。我们还证明了具有非常粗糙的初始数据的解的存在性$u_0 \in L^p，$$1 < p < \infty.$许多结果可以推广到更一般的一类方程，包括地表准地转方程。
The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian $\alpha < 1/2,$ and global existence as well as analyticity of solution for $\alpha \geq 1/2.$ We also prove the existence of solutions with very rough initial data $u_0 \in L^p,$ $1 < p < \infty.$ Many of the results can be extended to a more general class of equations, including the surface quasi-geostrophic equation.