On the linear problem related to the stability of uniformly rotating self-gravitating liquid

On the nonstationary motion of a viscous incompressible liquid over a rotating ball

“…The problems (3.7) and (3.8) in the domain bounded only by the surface G are treated in the paper [4] for other (greater) values of l. The proofs were somewhat incomplete, and we repeat here the main ideas of the proofs.…”

“…Proof of Theorem 3.3. We follow [4] and reduce the problem (3.8) to a similar problem with f = 0, v 0 = 0 and with f , d that can be extended by zero into F ×(−∞, 0) and G ×(−∞, 0) with preservation of class. We introduce v 1 = ∇Φ, where Φ is a solution of the Dirichlet-Neumann problem…”

“…write the estimates (4.27) obtained in neighborhoods of all x k and add them. We fix a sufficiently small λ and arrive at an inequality similar to (3.21) in [4]:…”