Sentence examples for a smooth solution to from inspiring English sources

Spectral convergence of the L2 least-squares functional and L2 error norms in space time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier Stokes equations.

Studying precisely the regularity of the force field created by the solution of the linear Vlasov-Fokker-Planck equation, we prove existence and uniqueness of a smooth solution to the Vlasov-Poisson-Fokker-Planck system in three dimensions.

Let ((rho,u)) be a smooth solution to the initial-boundary value problem (2.2).

Assume that is a smooth solution to (1.2) with initial data,, for.

Let w be a smooth solution to (L_epsilon w=f ) in (Qsubset mathbb {R}^{n+1}).

Wang and Zhao [12] established logarithmically improved blow-up criteria of a smooth solution to (1.1), (1.2) in the Morrey-Campanto space.

For 3D Navier-Stokes equations, whether there exists a global smooth solution to 3D impressible GMHD equations is still an open problem.

Let d be a local smooth solution to problem (1.23 - 1.25).

Let ((u,n,p)) be a local smooth solution to problem (1.1 - 1.6 1.1 - 1.6

By similar argument as that in [3, 4], it is easy to prove that there are and a unique smooth solution to the problem (1.3)–(1.9) in, and we only need to establish some a priori estimates for any time.

Li, Pan and Zhang [21, 22] proved the existence of a unique global smooth solution to the initial boundary value problem of 2D inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary.