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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.08273 |
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| _version_ | 1866916838529564672 |
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| author | Chen, Wenhui |
| author_facet | Chen, Wenhui |
| contents | We are interested in the global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson (JMGT) equations of Westervelt-type, namely, \begin{align*} τ\partial_t^3ψ+\partial_t^2ψ+\mathcal{A}ψ+(δ+τ)\mathcal{A}\partial_tψ=(1+\tfrac{B}{2A})\partial_t[(\partial_tψ)^2] \end{align*} in the whole space $\mathbb{R}^n$, with $τ,δ,\frac{B}{A}\in\mathbb{R}_+$ and the fractional Laplacian $\mathcal{A}:=(-Δ)^σ$ equipping $σ\in\mathbb{R}_+$. Our aims are twofold. For one thing, by considering the rough initial data with their Fourier support restrictions in a suitable subset of first octant, we demonstrate a global in-time existence result without requiring the smallness of initial data. For another, by removing these Fourier support restrictions, we prove another global in-time existence result for the equivalent strongly coupled JMGT systems, where the real and imaginary parts of initial data, respectively, belong to regular Sobolev spaces with different additional Lebesgue integrabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson equations of Westervelt-type under different conditions on initial data Chen, Wenhui Analysis of PDEs We are interested in the global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson (JMGT) equations of Westervelt-type, namely, \begin{align*} τ\partial_t^3ψ+\partial_t^2ψ+\mathcal{A}ψ+(δ+τ)\mathcal{A}\partial_tψ=(1+\tfrac{B}{2A})\partial_t[(\partial_tψ)^2] \end{align*} in the whole space $\mathbb{R}^n$, with $τ,δ,\frac{B}{A}\in\mathbb{R}_+$ and the fractional Laplacian $\mathcal{A}:=(-Δ)^σ$ equipping $σ\in\mathbb{R}_+$. Our aims are twofold. For one thing, by considering the rough initial data with their Fourier support restrictions in a suitable subset of first octant, we demonstrate a global in-time existence result without requiring the smallness of initial data. For another, by removing these Fourier support restrictions, we prove another global in-time existence result for the equivalent strongly coupled JMGT systems, where the real and imaginary parts of initial data, respectively, belong to regular Sobolev spaces with different additional Lebesgue integrabilities. |
| title | Global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson equations of Westervelt-type under different conditions on initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.08273 |