Blowup Criterion for Viscous Baratropic Flows with Vacuum States

By Xiangdi Huang, Jing Li, Zhouping Xin. 2010

147 citations recorded by the source corpus.

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/88298b4b440df0c6f5809211b8fb87fbe4ccd194

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In Applied Mathematics

1. Changyou Wang
2. Tao Huang
3. Huanyao Wen
4. T. Lamm
5. T. Rivière
6. Christoph Scheven
7. Andreas Gastel
8. F. Lin

Citations in the corpus

• Strong solutions of the compressible nematic liquid crystal flow (2011, methodology): “Now we briefly outline the main ideas of the proof, some of which are inspired by earlier works on the isentropic compressible Navier-Stokes equations by [3], [35], and [16].”