On the instability of solitary-wave solutions for fifth-order water wave models.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the integral representation of the solution to the Stokes system
On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold
On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the -particle Schrödinger equation. We assume the pair interaction is . For the interaction parameter , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for in [28]. This allows, in the case , for the application of the Klainerman–Machedon uniqueness theorem...
On the Korteweg-De Vries Equation.
On the Korteweg-de Vries equation: an associated equation.
On the -instability of fluid flows
On the -decay and local energy decay of solutions to nonlinear Klein-Gordon equations
On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case . Actually, we are interested in proving regularity results in spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced...
On the large order asymptotics of general states in semiclassical quantum mechanics
On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes
We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting...
On the linear force-free fields in bounded and unbounded three-dimensional domains
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the linear problem arising from motion of a fluid around a moving rigid body
We study a linear system of equations arising from fluid motion around a moving rigid body, where rotation is included. Originally, the coordinate system is attached to the fluid, which means that the domain is changing with respect to time. To get a problem in the fixed domain, the problem is rewritten in the coordinate system attached to the body. The aim of the present paper is the proof of the existence of a strong solution in a weighted Lebesgue space. In particular, we prove the existence...
On the local and global well-posedness theory for the KP-I equation
On the local strong solutions for a system describing the flow of a viscoelastic fluid
We consider a model for the viscoelastic fluid which has recently been studied in [4] and [1]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the above mentioned papers. The main difference in our approach is the use of the theory for the Stokes system.
On the local well-posedness of a Benjamin-Ono-Boussinesq system.
On the local well-posedness of the KP equations