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 reaction-diffusion-convection waves in unbounded strips.
Existence of semi-periodic solutions of steady Navier-Stokes equations in a half space with an exponential decay at infinity
Existence of solutions for a degenerate seawater intrusion problem.
Existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium
existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium
The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types of solutions are found: classical, critical and multivalued. Regularity of solutions is studied as well as their behavior depending on the size of the domain and on the coefficient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.
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 two-dimensional stationary Euler system for ideal fluids with arbitrary force
Existence of solutions of a nonlinear system modelling fluid flow in porous media.
Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary.
Existence of solutions vanishing near some axis for the nonstationary Stokes system with boundary slip conditions [Book]
Existence of strong solutions for nonisothermal Korteweg system
This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general...
Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Existence of time-periodic solutions to incompressible Navier-Stokes equations in the whole space.
Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Existence of weak solutions for a nonlinear elliptic system.
Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow.
Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions
We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided . To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.