Related papers: Surface shear waves in a half-plane with depth-var…
We consider the problem of the stability of the Navier-Stokes equations in $\mathbb{T}\times \mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \cite{greniernguyen}, the authors prove an $L^{\infty}$…
We consider the spectral function $\rho(\mu)$ $(\mu \geq 0)$ for the Sturm-Liouville equation $y^{''}+(\lambda-q)y =0$ on $[0,\infty)$ with the boundary condition $y(0)=0$ and where $q$ has slow decay $O(x^{-\alpha})$ $(a>0)$ as $x\to…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar…
In this paper we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semi-classical approach we are able to simplify this three-dimensional problem of the elastic wave…
In this study we analyze the phase and group velocity of three-dimensional linear traveling waves in two sheared flows, the plane channel and the wake flows. This was carried out by varying the wave number over a large interval of values at…
The background method is adapted to derive rigorous limits on surface speeds and bulk energy dissipation for shear stress driven flow in two and three dimensional channels. By-products of the analysis are nonlinear energy stability results…
The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind.…
We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In…
In this paper we deal with the exterior problem for a system of nonlinear wave equations in two space dimensions, assuming that the initial data is small and smooth. We establish the same type of lower bound of the lifespan for the problem…
Metal surfaces with disorder or with nanostructure modifications are studied, allowing for a localized charge layer (CL) in addition to continuous charges (CC) in the bulk, both charges having a compressional or diffusive non-local…
We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a $L^\infty$ family of global spatial plane wave solutions, which are connected with the two-dimensional…
This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…
We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation $\Delta u…
In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of traveling-wave solutions…
In this paper the time-fractional diffusion-wave equation with Riemman-Liouville fractional derivative is studied. The integral operators with the Wright function in the kernel, associated with the studied equation are introdused and their…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
We consider the free boundary problem for a plasma--vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not…