## Search

Now showing items 1-10 of 35

#### Correlation imaging in inverse scattering is tomography on probability distributions

(Inverse Problems, 2018-12-04)

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...

#### Determination of convection terms and quasi-linearities appearing in diffusion equations

(2018-12)

We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...

#### Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane

(2018-12)

For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...

#### Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations

(Journal of Mathematical Analysis and Applications, 2018-10)

We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...

#### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids

(Journal of Differential Equations, 2018-09)

We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...

#### Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates

(Mathematische Annalen, 2018-09)

We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...

#### Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7

(Comptes Rendus Mathematique, 2018-09-01)

For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...

#### Vector-valued operators, optimal weighted estimates and the $C_p$ condition

(Science China Mathematics, 2018-09)

In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...

#### Weighted norm inequalities for rough singular integral operators

(Journal of Geometric Analysis, 2018-08-17)

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...

#### Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals

(Archive for Rational Mechanics and Analysis, 2018-08-10)

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...