Some relatively new techniques for nonlinear problems.
Some remarks on gradient estimates for heat kernels.
Some remarks on Prandtl system
The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.
Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Some remarks on the continuity equation
This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.
Some solutions for a class of singular equations
In this paper we obtain all solutions which depend only on for a class of partial differential equations of higher order with singular coefficients.
Some weighted Hardy-type inequalities on anisotropic Heisenberg groups.
Sophus Lie a harmonie v matematické fyzice (k 150. výročí narození)
Source type positive solutions of nonlinear parabolic inequalities
Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p
We establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C0([0, T]; Lp(Ω)) by introducing appropriate time-weighted Lebesgue norms inspired by a priori estimates of solutions. This framework allows us to obtain global existence of solutions under the proviso that initial...
Space-time variational saddle point formulations of Stokes and Navier–Stokes equations
The instationary Stokes and Navier−Stokes equations are considered in a simultaneously space-time variational saddle point formulation, so involving both velocities u and pressure p. For the instationary Stokes problem, it is shown that the corresponding operator is a boundedly invertible linear mapping between H1 and H'2, both Hilbert spaces H1 and H2 being Cartesian products of (intersections of) Bochner spaces, or duals of those. Based on these results, the operator that corresponds to the Navier−Stokes...
Stability of classes of mappings and Hölder continuity of higher derivatives of elliptic solutions to systems of nonlinear differential equations.
Stability of peakons for the generalized Camassa-Holm equation.
Stability of solitary waves for a system of nonlinear Schrödinger equations with three wave interaction
Stability of solitary waves for derivative nonlinear Schrödinger equation
Stability of solutions for an abstract Dirichlet problem
We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.
Stabilization of Schrödinger equation in exterior domains
We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.
Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems.
Straightening of a noncylindrical region and evolution equations
Strichatz inequalities with weights in Morrey-Campanato classes.