Analysis of singularity of solutions to the Navier-Stokes equations

在压力条件下，证明了N-S方程弱解的正则性。特别地，在基于Lorentz空间的尺度不变空间中，当压力足够小时，我们排除了爆破的可能性。如果磁场和压强都属于基于小范数洛伦兹空间的标度不变空间，则这一结果也适用于MHD方程。

We prove regularity of weak solutions to the Navier-Stokes equations under the conditions on the pressure. In particular, we exelude the possibility of blow-up in the case that the pressure is small enough in scaling invariant spaces based on Lorentz spaces. This result can be applied to MHD equations if the magnetic field in addition to the pressure belongs to the scaling invariant spaces based on the Lorentz spaces with small norms.