We consider the Navier‐Stokes equations for viscous incompressible flows in the half‐plane
under the no‐slip boundary condition. By using the vorticity formulation we prove the local …

Let the viscosity ε→ 0 ε→0 for the 2D steady Navier‐Stokes equations in the region 0≤ x≤
L 0≤x≤L and 0≤ y<∞ 0≤y<∞ with no slip boundary conditions at y= 0 y=0. For L<< 1 …

We address the local well-posedness of the Prandtl boundary layer equations. Using a new
change of variables we allow for more general data than previously considered, that is, we …

We find a new class of data for which the Prandtl boundary layer equations and the
hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl …

We show the H 1 stability of shear flows of Prandtl type: U^ ν=\left (U_s (y/ν), 0\right) U ν= U s
(y/ν), 0, in the steady two-dimensional Navier–Stokes equations, under the natural …

Complex topographies exhibit universal properties when fluvial erosion dominates
landscape evolution over other geomorphological processes. Similarly, we show that the …

We consider the convergence in the $ L^ 2$ norm, uniformly in time, of the Navier-Stokes
equations with Dirichlet boundary conditions to the Euler equations with slip boundary …

Singular perturbations occur when a small coefficient affects the highest order derivatives in
a system of partial differential equations. From the physical point of view, singular …

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes
equations modeling viscous incompressible flows converge to solutions of the Euler …

Let the viscosity $\varepsilon\rightarrow 0$ for the 2D steady Navier-Stokes equations in the
region $0\leq x\leq L $ and $0\leq y<\infty $ with no slip boundary conditions at $ y= 0$. For …