Related papers: Transport equation in generalized Campanato spaces
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…
We construct a large class of examples of non-uniqueness for the linear transport equation and the transport-diffusion equation with divergence-free vector fields in Sobolev spaces $W^{1,p}$.
We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and…
We study the stochastic transport equation with globally $\beta$-H\"older continuous and bounded vector field driven by a non-degenerate pure-jump L\'evy noise of $\alpha$-stable type. Whereas the deterministic transport equation may lack…
In the paper, we study the Prandtl system with initial data admitting non-degenerate critical points. For any index $\sigma\in[3/2, 2],$ we obtain the local in time well-posedness in the space of Gevrey class $G^\sigma$ in the tangential…
We consider the stochastic transport linear equation and we prove existence and uniqueness of weak $L^{p}-$solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only…
Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant…
In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
The Einstein's field equations of Friedmann-Robertson-Walker universes filled with a dissipative fluid described by both the {\em truncated} and {\em non-truncated} causal transport equations are analyzed using techniques from dynamical…
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one dimensional model of the surface quasi-geostrophic equation and the…
Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is 1-Lipschitz. Owing to its many applications in analysis, probability, and…
For $ p\in (1, \infty)$, we consider the following weighted Neumann eigenvalue problem on $B_1^c$, the exterior of the closed unit ball in $R^N$: \begin{equation}\label{Neumann eqn} \begin{aligned} -\Delta_p \phi & = \lambda g |\phi|^{p-2}…
In this paper, we prove the well-posedness for the fractional Navier-Stokes equations in critical spaces $G^{-(2\beta-1)}_{n}(\mathbb{R}^{n})$ and $BMO^{-(2\beta-1)}(\mathbb{R}^{n}).$ Both of them are close to the largest critical space…
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has…
Some classical mass transportation problems are investigated in a finitely additive setting. Let $\Omega=\prod_{i=1}^n\Omega_i$ and $\mathcal{A}=\otimes_{i=1}^n\mathcal{A}_i$, where $(\Omega_i,\mathcal{A}_i,\mu_i)$ is a ($\sigma$-additive)…
The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…
For the famous Camassa-Holm equation, the well-posedness in $B^{1+\frac{1}{p}}_{p,1}(\mathbb{R})$ with $1\leq p\leq2$ and the ill-posedness in $B^{1+\frac{1}{p}}_{p,r}(\mathbb{R})$ with $1\leq p\leq+\infty,\ 1<r\leq+\infty$ had been studied…
$f(T)$ gravity offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution…
We consider a non-local boundary value problem for the Laplace equation in unbounded studding the weak and strong solvability of that problem in the framework of the weighted Sobolev space $W^{1,p}_\nu$, with a Muckenhoupt weight. We proved…