In this paper,we study the dynamical stability of a family of explicit blowup solutions of the threedimensional(3D)incompressible Navier-Stokes(NS)equations with smooth initial values,which is constructed in Guo et al...In this paper,we study the dynamical stability of a family of explicit blowup solutions of the threedimensional(3D)incompressible Navier-Stokes(NS)equations with smooth initial values,which is constructed in Guo et al.(2008).This family of solutions has finite energy in any bounded domain of R3,but unbounded energy in R3.Based on similarity coordinates,energy estimates and the Nash-Moser-H?rmander iteration scheme,we show that these solutions are asymptotically stable in the backward light-cone of the singularity.Furthermore,the result shows the existence of local energy blowup solutions to the 3D incompressible NS equations with growing data.Finally,the result also shows that in the absence of physical boundaries,the viscous vanishing limit of the solutions does not satisfy the 3D incompressible Euler equations.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12231016 and 12071391)Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515010860)。
文摘In this paper,we study the dynamical stability of a family of explicit blowup solutions of the threedimensional(3D)incompressible Navier-Stokes(NS)equations with smooth initial values,which is constructed in Guo et al.(2008).This family of solutions has finite energy in any bounded domain of R3,but unbounded energy in R3.Based on similarity coordinates,energy estimates and the Nash-Moser-H?rmander iteration scheme,we show that these solutions are asymptotically stable in the backward light-cone of the singularity.Furthermore,the result shows the existence of local energy blowup solutions to the 3D incompressible NS equations with growing data.Finally,the result also shows that in the absence of physical boundaries,the viscous vanishing limit of the solutions does not satisfy the 3D incompressible Euler equations.
