Related papers: Global solutions for the generalized SQG equation …
In this work, we investigate the blow-up of solutions to the generalized surface quasi-geostrophic (gSQG) equation in $\mathbb{R}^{2}$, within the more singular range $\beta\in(1,2)$ for the coupling of the velocity field. This behavior is…
We consider the problem of finding a solution to the incompressible Euler equations $$ \omega_t + v\cdot \nabla \omega = 0 \quad \hbox{ in } \mathbb{R}^2 \times (0,\infty), \quad v(x,t) = \frac 1{2\pi} \int_{{\mathbb R}^2} \frac…
We study the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. We…
The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invarint solution for it are obtained by means of this technique. Polynomial, trigonometric and elliptic function solutions can be…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for spherically symmetric motion. We establish a unified method…
We extend the search for traveling-wave asymptotic solutions of the non-linear Balitsky-Kovchegov (BK) saturation equation to non-forward dipole-target amplitudes. Making use of conformal invariant properties of the…
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the $\mathrm{tanh}$-method. The method works by…
New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross-Pitaevskii equation \begin{equation*} i\Psi_t= \Delta \Psi+(1-|\Psi|^2)\Psi, \end{equation*} where $\Psi$ is a complex valued…
Global regular axially symmetric solutions with large swirl in a cylinder with periodic conditions on the top and on the bottom are proved. On the lateral part of its boundary the boundary slip conditions are assumed. The proof is obtained…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
This paper consists of three results on pattern formation of Ginzburg-Landau $m$-armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely describe the global bifurcation diagram of vortex…
This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high-dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the…
We establish the existence of quasi-periodic traveling wave solutions for the $\beta$-plane equation on $\mathbb{T}^2$ with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…
We present new periodic, kink-like and soliton-like travelling wave solutions to the hyperbolic generalization of Burgers equation. To obtain them, we employ the classical and generalized symmetry methods and the ansatz-based approach
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…