Tootfinder

No ceasefire, possible land swaps, vague security guarantees: Everything we know following Trump’s meeting with Putin: https://benborges.xyz/2025/08/16/no-ceasefire-possible-land-swaps.html

Regularizing Effect for a Nonlocal Maxwell-Schr\"odinger System
Lu\'is Henrique de Miranda, Ayana Pinheiro de Castro Santana
https://arxiv.org/abs/2507.12294

Regularizing Effect for a Nonlocal Maxwell-Schrödinger System
In this paper we prove existence and regularity of weak solutions for the following system \begin{align*} \begin{cases} &-\mbox{div}\Bigg(\bigg(\|\nabla u\|^{p}_{L^{p}}+\|\nabla v\|^{p}_{L^{p}}\bigg)|\nabla u|^{p-2}\nabla u\Bigg) + g(x,u,v)=f \ \ \ \mbox{in} \ Ω; &-\mbox{div}\Bigg(\bigg(\|\nabla u\|^{p}_{L^{p}}+\|\nabla v\|^{p}_{L^{p}}\bigg)|\nabla v|^{p-2}\nabla v\Bigg) = h(x,u,v) \ \ \ \ \mbox{in} \ Ω; &u=v=0 \ \mbox{on} …

US House advances a trio of cryptocurrency bills following over nine hours of private talks on Wednesday, a day after Trump intervened to save the initiative (Reuters)
https://www.reuters.com/legal/government/us-house-clears-p…

$L^2$-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Shijie Shang, Pengyu Wang, Tusheng Zhang
https://arxiv.org/abs/2509.12744

$L^2$-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t,x)) + σ(u(t,x))W(dt,dx) $$ for $t > 0$ and $x \in [0,1]$, with initial condition $$ u(0,x) = u_0(x) $$ for $x \in [0,1]$, where $u_0 \in L^2[0,1]$. In this paper, we establish existence and uniqueness of probabilistically strong solutions in $C(R_+, L^2[0,1])$. Our result resolves a problem from [Ann. Probab. 47 (…

US officials provide contradictory statements on security guarantees, fueling uncertainty ahead of Trump-Zelensky meeting: https://benborges.xyz/2025/08/17/us-officials-provide-contradictory-statements.html

📉 Fears that falling birth rates in the US could lead to population collapse are based on faulty assumptions
https://phys.org/news/2025-07-falling-birth-population-collapse-based.html

Fears that falling birth rates in the US could lead to population collapse are based on faulty assumptions
Pronatalism—the belief that low birth rates are a problem that must be reversed—is having a moment in the U.S.

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo
https://arxiv.org/abs/2507.11203 htt…

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
In this paper, we study the existence and nonrelativistic limit of normalized ground states for the following nonlinear Dirac equation with power-type potentials \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3α_k\partial_k u +mc^2 β{u}- |{u}|^{p-2}{u}=ω{u}, \\ &\displaystyle\int_{\mathbb{R}^3}\vert u \vert^2 dx =1. \end{cases} \end{equation*} We demonstrate the existence of ground states for large $c$ and establish the uniqueness of the associated Lagrange multiplier f…

Space-time fractional stochastic partial differential equations driven by L\'evy white noise
Yuhui Guo, Jiang-Lun Wu
https://arxiv.org/abs/2506.12834 h…

Space-time fractional stochastic partial differential equations driven by Lévy white noise
This paper is concerned with the following space-time fractional stochastic nonlinear partial differential equation \begin{equation*} \left(\partial_t^β+\fracν{2}\left(-Δ\right)^{α/ 2}\right) u=I_{t}^γ\Big[ f(t,x,u)-\sum_{i=1}^{d} \frac{\partial}{\partial x_i} q_i(t,x,u)+ σ(t,x,u) F_{t,x}\Big] \end{equation*} for a random field $u(t,x):[0,\infty)\times\mathbb{R}^d \mapsto\mathbb{R}$, where $α>0, β\in(0,2), γ\ge0, ν>0, F_{t,x}$ is a Lévy space-time white noise, $I_{t}^γ$ stands for…

Construction of solutions for a critical elliptic system of Hamiltonian type
Congzheng Xuanyuan, Tingfeng Yuan, Yuxia Guo
https://arxiv.org/abs/2509.11251 https://

Construction of solutions for a critical elliptic system of Hamiltonian type
We consider the following nonlinear elliptic system of Hamiltonian type with critical exponents: \begin{equation*}\left\{\begin{align*} -Δu + V(|y'|,y'') u = v^p, \;\; \text{in} \;\; \mathbb{R}^N,\\ -Δv + V(|y'|,y'') v = u^q, \;\; \text{in} \;\; \mathbb{R}^N,\\ u, v > 0 , (u,v) \in (\dot{W}^{2,\frac{p+1}{p}} (\mathbb{R}^N) \cap L^2(\mathbb{R}^N)) \times (\dot{W}^{2,\frac{q+1}{q}} (\mathbb{R}^N) \cap L^2(\mathbb{R}^N)) ,\end{align*}\right. \end{equation*} where $(y', …

A degree-counting formula for a Keller-Segel equation on a surface with boundary
Mohameden Ahmedou, Zhengni Hu, Heming Wang
https://arxiv.org/abs/2506.12783

A degree-counting formula for a Keller-Segel equation on a surface with boundary
In this paper, we consider the following Keller-Segel equation on a compact Riemann surface $(Σ, g)$ with smooth boundary $\partialΣ$: \[ -Δ_g u = ρ\Big(\frac{V e^u}{\int_Σ V e^u \mathrm{d} v_g} - \frac{1}{|Σ|_g}\Big) \text{ in } Σ, \quad \text{ with } \partial_{ν_g} u = 0 \text{ on } \partial Σ, \] where $V$ is a smooth positive function on $Σ$ and $ρ> 0$ is a parameter. We perform a refined blow-up analysis of bubbling solutions and establish sharper a priori esti…