Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in dimensions
Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity.
Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations.
Existence of entropy solutions for a reacting Euler system.
Existence of Local Smooth Solution for a Generalized Zakharov System.
Existence of local solutions for free boundary problems for viscous compressible barotropic fluids
We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
Existence of minimizers for Kohn-Sham models in quantum chemistry
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.
Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.
Existence of permanent and breaking waves for a shallow water equation : a geometric approach
The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...
Existence of pullback attractors for the coupled suspension bridge equations.
Existence of reaction-diffusion-convection waves in unbounded strips.
Existence of regular solutions to the stationary Navier-Stokes equations.
Existence of regular solutions to the steady Navier-Stokes equations in bounded six-dimensional domains
Existence of semi-periodic solutions of steady Navier-Stokes equations in a half space with an exponential decay at infinity
Existence of solutions for an Oldroyd model of viscoelastic fluids.
Existence of solutions for compressible fluid models of Korteweg type
Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.
Existence of solutions for the two-dimensional stationary Euler system for ideal fluids with arbitrary force