arXiv subjects

Fuzhou Wu

Publications and source records attributed to Fuzhou Wu.

5 recordsLinked to original sources

arXiv2016

Regularity Structure, Vorticity Layer and Convergence Rates of Inviscid Limit of Free Surface Navier-Stokes Equations with or without Surface Tension

In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes equations and the existence of strong or weak vorticity layer for different conditions. When the limit of the difference between the initial Navier-Stokes vorticity and the initial Euler vorticity is nonzero, or the tangential projection on the free surface of the Euler strain tensor multiplying by normal vector is nonzero, there exists a strong vorticity layer. Otherwise, the vorticity layer is weak. We estimate convergence rates of tangential derivatives and the first order standard normal derivative in energy norms, we show that not only tangential derivatives and standard normal derivative have different convergence rates, but also their convergence rates are different for different Euler boundary data. Moreover, we determine regularity structure of the free surface Navier-Stokes solutions with or without surface tension, surface tension changes regularity structure of the solutions.

math.AP↗

arXiv2016

Full Regularity and Well-Posedness of the Nonlinear Unsteady Prandtl Equations with Robin or Dirichlet Boundary Condition

In this paper, we study the full regularity and well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin or Dirichlet boundary condition in half space. Under Oleinik's monotonicity assumption, we prove the large time existence of classical solutions to the nonlinear Prandtl equations with Robin or Dirichlet boundary condition, when both initial vorticity and the general Euler flow are sufficiently small. For the general Euler flow, the vertical velocity of the Prandtl flow is unbounded. We prove that the Prandtl solutions preserve the full regularities in our solution spaces. The uniqueness and stability are also proved in the weighted Sobolev spaces.

math.AP↗

arXiv2015

Well-Posedness of the Nonlinear Unsteady Prandtl Equations with Robin Boundary Condition in Weighted Sobolev Spaces

In this paper, we study the well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin boundary condition in half space in weighted Sobolev spaces. We firstly investigate the monotonic shear flow with Robin boundary condition and the linearized Prandtl-type equations with Robin boundary condition in weighted Sobolev spaces. Due to the degeneracy of the Prandtl equations and the loss of regularity, we apply the Nash-Moser-Hormander iteration scheme to prove the existence of classical solutions to the nonlinear Prandtl equations with Robin boundary condition when the initial data is a small perturbation of a monotonic shear flow satisfying Robin boundary condition. The uniqueness and stability are also proved in the weighted Sobolev spaces. The nonlinear Prandtl equations with Robin boundary arise in the inviscid limit of incompressible Navier-Stokes equations with Navier-slip boundary condition for which the slip length is square root of viscosity. Our results are also valid for the Dirichlet boundary case.

math.AP↗

arXiv2014

Initial Layer and Relaxation Limit of Non-Isentropic Compressible Euler Equations with Damping

In this paper, we study the relaxation limit of the relaxing Cauchy problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We prove that the velocity of the relaxing equations converges weakly to that of the relaxed equations, while other variables of the relaxing equations converges strongly to the corresponding variables of the relaxed equations. We show that as relaxation time approaches 0, there exists an initial layer for the ill-prepared data, the convergence of the velocity is strong outside the layer; while there is no initial layer for the well-prepared data, the convergence of the velocity is strong near t=0.

math.AP↗

arXiv2014

Global Existence and Nonlinear Diffusion of Classical Solutions to Non-Isentropic Euler Equations with Damping in Bounded Domain

We considered classical solutions to the initial boundary value problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We obtained global a priori estimates and global existence results of classical solutions to both non-isentropic Euler equations with damping and their nonlinear diffusion equations under small data assumption. We proved the pressure and velocity decay exponentially to constants, while the entropy and density can not approach constants. Finally, we proved the pressure and velocity of the non-isentropic Euler equations with damping converge exponentially to those of their nonlinear diffusion equations when the time goes to infinity.

math.AP↗