Mean curvature flow with free boundary – Type 2 singularities
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DOI: 10.1002/mana.201800156
Abstract: In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only… read more here.
Keywords: mean curvature; free boundary; type singularities; curvature flow ... See more keywords
On scaling invariance and type-I singularities for the compressible Navier-Stokes equations
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DOI: 10.1007/s11425-018-9363-1
Abstract: We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-I singularities of solutions with $$\mathop {\lim \sup }\limits_{t \nearrow T} |div(t,x)|(T - t) \leqslant \kappa $$limsupt↗T|div(t,x)|(T−t)≤κ can… read more here.
Keywords: compressible navier; invariance; type singularities; stokes equations ... See more keywords