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math.AP2026
Stratification and rectifiability of harmonic map flows via tangent measures
Haotong Fu, Wei Wang, Ke Wu +1
In this paper, we investigate the stratification theory for ``suitable solutions" of harmonic map flows based on the spatial symmetry of tangent measures. Building on the quantitat…
math.AP2026
Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators
Shaoxiong Chen, Hichem Hajaiej, Min Yang +1
We study the Choquard equation involving mixed local and nonlocal operators \[ -Îu + (-Î)^{s}u + V(x)u = \left(\frac{1}{|x|^μ} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}…
math.AP2026★ 1 cited
Low-regularity well-posedness for a mixed-sign quadratic Dirac equation on -star metric graphs
Huichao Xing, Zhipeng Yang
We study the Cauchy problem for a mixed-sign quadratic Dirac equation on a noncompact -star metric graph , \[ \mathrm{i}\partial_t Ï= DÏ- \mathcal N(Ï), \qquad Ï(0)=Ï_0,…