4 papers
Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space
Genqian Liu
Based on the essential connection of the parabolic inertia Lamé equations and Navier-Stokes equations, we prove the existence of smooth solutions of the incompressible Navier-Stoke…
Eigenvalue inequalities and three-term asymptotic formulas of the heat traces for the Lamé operator and Stokes operator
Genqian Liu
This paper is devoted to establish the most essential connections of the eigenvalue problems for the Laplace operator, Lamé operator, Stokes operator, buckling operator and clamped…
Spectral asymptotics for linear elasticity with mixed boundary conditions
Genqian Liu
In this note, we shall show that the two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions which were given by Capoferri and Mann in \c…
On an algorithm for two-term spectral asymptotic formulas
Genqian Liu
In the book [Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators, Amer. Math. Soc., Providence, RI, 1997], a key and central…