An existence result in nonlinear theory of electromagnetic fields
This paper is concerned with the nonlinear theory of equilibrium for materials which do not conduct electricity. An existence and uniqueness result is established.
An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions
The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends...
An existence theorem for the v. Kármán equations under the condition of free boundary
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
An explicit potential theory for the stokes resolvent boundary value problems in three dimensions.
An explicit right inverse of the divergence operator which is continuous in weighted norms
The existence of a continuous right inverse of the divergence operator in , 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals...
An explicit solution of coupled viscous Burgers' equation by the decomposition method.
An ill posed Cauchy problem for a hyperbolic system in two space dimensions
An improved maximal inequality for 2D fractional order Schrödinger operators
The local maximal operator for the Schrödinger operators of order α > 1 is shown to be bounded from to L² for any s > 3/8. This improves the previous result of Sjölin on the regularity of solutions to fractional order Schrödinger equations. Our method is inspired by Bourgain’s argument in the case of α = 2. The extension from α = 2 to general α > 1 faces three essential obstacles: the lack of Lee’s reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable...
An improved regularity criteria for the MHD system based on two components of the solution
As observed by Yamazaki, the third component of the magnetic field can be estimated by the corresponding component of the velocity field in
An initial boundary value problem for Maxwell's equations in a parabolic limit case.
An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid
The Dirac equation for spinor-valued fields on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet of the hyperboloid. In particular, we derive an integral formula expressing the value of in a chosen point as an integral over a compact cycle given by the intersection of the null cone with in the Minkowski space .
An interacting particles process for Burgers equation on the circle.
An interpretation of the Vakulenko-Kapitanskiĭ estimate.
An introduction to probabilistic methods with applications
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....
An introduction to the Einstein-Vlasov system
An inverse problem for a nonlinear Schrödinger equation.
An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.
An isoperimetric bound for a Sobolev constant
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.