5 citations · 8 across the 6 of their papers we have counts for
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Weak solutions of 3D compressible Navier-Stokes equations in critical case
Pavel I. Plotnikov
New estimates of the potentials of solutions to the compressible Navier-Stokes equations are derived. The result obtained are applied to boundary value problems for the compressibl…
A Proof of Hélein's Conjecture on Boundedness of Conformal Factors when n=3
P. I. Plotnikov, J. F. Toland
For smooth mappings of the unit disc into the oriented Grassmannian manifold , Hélein (2002) conjectured the global existence of Coulomb frames with bounded confor…
Isothermal Navier-Stokes Equations and Radon Transform
P. I. Plotnikov, W. Weigant
In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a pro…
Steady 3D viscous compressible flows with adiabatic exponent
P. I. Plotnikov, W. Weigant
The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satis…
Small divisor problem in the theory of three-dimensional water gravity waves
Gérard Iooss, Pavel I. Plotnikov
We consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity and resulting from the nonlinear interaction of two s…