Finite time singularities and global well-posedness for fractal Burgers equations Hongjie DongDapeng DuDening Li 35Q3582C70Burgers equationfinite-time singularitiesglobal well-posednessspatial analyticity Burgers equations with fractional dissipation on $\mathbb{R}\times\mathbb{R}^{+}$ or on $\mathbb{S}^1\times\mathbb{R}^{+}$ are studied. In the supercritical dissipative case, we show that with very generic initial data, the equation is locally well-posed and its solution develops gradient blow-up in finite time. In the critical dissipative case, the equation is globally well-posed with arbitrary initial data in $H^{1/2}$. Finally, in the subcritical dissipative case, we prove that with initial data in the scaling-invariant Lebesgue space, the equation is globally well-posed. Moreover, the solution is spatial analytic and has optimal Gevrey regularity in the time variable. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3505 10.1512/iumj.2009.58.3505 en Indiana Univ. Math. J. 58 (2009) 807 - 822 state-of-the-art mathematics http://iumj.org/access/