Related papers: Existence and Uniqueness for McKean-Vlasov equatio…

This paper is a continuation of [26]. Here theorems on conditional uniqueness and regularity for solutions to stochastic Navier-Stokes equations in $\mathbb R^d$ are presented.

We study the tamed magnetohydrodynamics equations, introduced recently in a paper by the author, perturbed by multiplicative Wiener noise of transport type on the whole space $\mathbb{R}^{3}$ and on the torus $\mathbb{T}^{3}$. In a first…

By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular…

For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…

We consider a path-dependent Hamilton--Jacobi equation with coinvariant derivatives over the space of continuous functions. We prove two uniqueness results for viscosity (generalized) solutions defined in terms of coinvariantly smooth test…

We study uniqueness properties of solutions of Schr\"odinger equations. The aim is to obtain sufficient conditions on the decay behavior of the difference of two solution $u_1-u_2$ of the equation at two different times $t_0=0$ and $t_1=1$…

We study the Bellman equation in the Wasserstein space arising in the study of mean field control problems, namely stochastic optimal control problems for McKean-Vlasov diffusion processes.Using the standard notion of viscosity solution \`a…

In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…

We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$

We study differential equations with piecewise constant argument (DEPCA) and establish the existence and uniqueness of remotely almost periodic (RAP) solutions for \[ x'(t)=A(t)x(t)+B(t)x([t])+f(t). \] Under an exponential dichotomy for the…

We consider the evolutionary Hamilton-Jacobi equation \begin{align*} w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \quad(x,t)\in M\times [0,+\infty), \end{align*} where $M$ is a compact manifold, $H:T^*M\times R\to R$, $H=H(x,p,u)$ satisfies Tonelli…

Non-geometric flux vacua have recently been revisited, leading to the remarkable discovery of isolated 4D ${\mathcal N}=1$ supersymmetric Minkowski vacua. These constructions rely on the non-renormalization of the superpotential, which is…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

We develop an existence, uniqueness and regularity theory for general multidimensional strongly coupled FBSDE using so called decoupling fields. We begin with a local result and extend it to a global theory via concatenation. The…

In this paper, we study the following supercritical McKean-Vlasov SDE, driven by a symmetric non-degenerate cylindrical $\alpha$-stable process in $\mathbb{R}^d$ with $\alpha \in (0,1)$: $$ \mathord{{\rm d}} X_t = (K *…

If $U:[0,+\infty[\times M$ is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation $$\partial_tU+ H(x,\partial_xU)=0,$$ where $M$ is a not necessarily compact manifold, and $H$ is a Tonelli Hamiltonian, we…

In the study of equisingularity of isolated singularities we have the classical theorem of Briancon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the…

We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…

In this paper we consider the linearized version of a system of partial differential equations arising from a fluid-structure interaction model. We prove the existence and the uniqueness of the solution under natural regularity assumptions.

This paper is concerned with the existence and uniqueness of positive solution for the fourth order Kirchhoff type problem $$\left\{\begin{array}{ll} u''''(x)-(a+b\int_0^1(u'(x))^2dx)u''(x)=\lambda f(u(x)),\ \ \ \ x\in(0,1),\\…