Navier-Stokes Equations with Degenerate Viscosity, Vacuum and Gravitational Force

In this article we want to study some problems related with the role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations.. Before

Thus, roughly speaking, Theorem 2 extends the uniqueness results of Prodi, Serrin, Sohr and von Wahl to some classes of weak solutions which.. are more regular in

Keywords: Navier–Stokes equations; Uniqueness; Weak solution; Fourier localization; Losing derivative estimates.. In three dimensions, however, the question of regularity and

There also exists a nonlinear generalized form of the Navier’s conditions.. Fujita has studied the Stokes model with those nonlinear boundary conditions, a well-posed problem leading

– (1) Condition (1.1) appearing in the statement of Theorem 1 should be understood as a nonlinear smallness condition on the initial data: the parameter A, measuring through (H1)

Coron has derived rigorously the slip boundary condition (1.3) from the boundary condition at the kinetic level (Boltzmann equation) for compressible uids. Let us also recall that

In order to prove the above existence and uniqueness results for (IN S ) supplemented with data satisfying just (1.8), the main difficulty is to propagate enough regularity for

In [4]-[6] classes of initial data to the three dimensional, incompressible Navier- Stokes equations were presented, generating a global smooth solution although the norm of the