Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces
In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqu...
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2025-05-01
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| Series: | Fractal and Fractional |
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| author | Muhammad Zainul Abidin Abid Khan |
| author_facet | Muhammad Zainul Abidin Abid Khan |
| author_sort | Muhammad Zainul Abidin |
| collection | DOAJ |
| description | In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqueness of a global mild solution for small and divergence-free initial data. Moreover, our approach is based on proving sharp bilinear convolution estimates in critical Sobolev norms, which in turn guarantee the uniform analyticity of both the velocity and magnetic fields with respect to time. Furthermore, leveraging the decay properties of the associated fractional heat semigroup and a bootstrap argument, we derived algebraic decay rates and established the long-time dissipative behavior of FrMHD solutions. These results extended the existing literature on fractional Navier–Stokes equations by fully incorporating magnetic coupling and Coriolis effects within a unified fractional-dissipation framework. |
| format | Article |
| id | doaj-art-e5f1eb68ee4345cf83cd623bf659784f |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-e5f1eb68ee4345cf83cd623bf659784f2025-08-20T03:24:38ZengMDPI AGFractal and Fractional2504-31102025-05-019636010.3390/fractalfract9060360Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev SpacesMuhammad Zainul Abidin0Abid Khan1School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaSchool of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaIn this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqueness of a global mild solution for small and divergence-free initial data. Moreover, our approach is based on proving sharp bilinear convolution estimates in critical Sobolev norms, which in turn guarantee the uniform analyticity of both the velocity and magnetic fields with respect to time. Furthermore, leveraging the decay properties of the associated fractional heat semigroup and a bootstrap argument, we derived algebraic decay rates and established the long-time dissipative behavior of FrMHD solutions. These results extended the existing literature on fractional Navier–Stokes equations by fully incorporating magnetic coupling and Coriolis effects within a unified fractional-dissipation framework.https://www.mdpi.com/2504-3110/9/6/360fractional rotating magnetohydrodynamicscritical Sobolev spaceswell-posednessuniform analyticitytime-decay rates |
| spellingShingle | Muhammad Zainul Abidin Abid Khan Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces Fractal and Fractional fractional rotating magnetohydrodynamics critical Sobolev spaces well-posedness uniform analyticity time-decay rates |
| title | Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces |
| title_full | Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces |
| title_fullStr | Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces |
| title_full_unstemmed | Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces |
| title_short | Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces |
| title_sort | uniform analyticity and time decay of solutions to the 3d fractional rotating magnetohydrodynamics system in critical sobolev spaces |
| topic | fractional rotating magnetohydrodynamics critical Sobolev spaces well-posedness uniform analyticity time-decay rates |
| url | https://www.mdpi.com/2504-3110/9/6/360 |
| work_keys_str_mv | AT muhammadzainulabidin uniformanalyticityandtimedecayofsolutionstothe3dfractionalrotatingmagnetohydrodynamicssystemincriticalsobolevspaces AT abidkhan uniformanalyticityandtimedecayofsolutionstothe3dfractionalrotatingmagnetohydrodynamicssystemincriticalsobolevspaces |