Abstract. The procedure of solving the system of the Navier-Stokes equations is proposed. The initial conditions: the velocity divergence (dilatation) being zero and the temperature being the known function, the initial density being constant. The problem is set in the infinite space. The solution of the Navier-Stokes equations was reduced to the solution of integral equations of the Volterra t...

In this paper, we study the 3D axisymmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some Lp norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction bet...

This paper gives an example of a periodic, smooth, divergencefree initial vector field and a periodic and bounded external force such that there exist a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions but the solution cannot be continued to the whole space. The example also shows that the solutions to the Navier-Stokes equation...

There exist complex behavior of the solution to 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on isentropic with constant viscosity coefficient x , t ∈ open="[" 0 + ∞ × ...

We consider dynamics system with damping, which are obtained by some transformations from the system of incompressible Navier-Stokes equations. These have similar properties to original Navier-Stokes equations the scaling invariance. Due to the presence of the damping term, conclusions are different with proving the origin of the incompressible Navier-Stokes equations and get some new conclusio...

We investigate the zero dissipation limit problem of the one dimensional compressible non–isentropic Navier–Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution of the Navier–Stokes equations exists for all time, and converge to the Riemann solution of the corresponding Euler equations with the same Riemann initial...

Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

In this talk we address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions...

We present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier Stokes equations in R. The method, based on so-called Gevrey estimates, also yields explicit bounds on the growth of the radius of analyticity of the solution in time. Moreover, under the assumption that the Navier Stokes solution stays sufficiently close to a solution of th...